The MIT soccer team has 2 games scheduled for one weekend. It has a 0.4 probability of not losing the first game. and a 0.7 probability of not losing the second game, independent of the first. If it does not lose a particular game, the team is equally likely to win or tie. independent of what happens in the other game. The MIT team will receive 2 points for a win, 1 for a tie. and 0 for a loss. Find the PMF of the number of points that the team earns over the weekend.

Answers

Answer 1

Answer:

Step-by-step explanation:

To determine the PMF of the points that the team receive, we must determine the probabilities of winning each of the games.

Consider the firt game. We know that the probability of not losing is 0.4. Since the team can either lose the game or not, we have that the probability of losing it is 0.6. We are told that given that the team does not lose, the probability of winning or having a tie is the same. Recall that, given events A, B, the conditional probability P(A|B) (which means probability of A given B) is given as

[tex]P(A|B) = \frac{P(A\cap B)}{P(B)}[/tex]

in our case, we have that B:= not losing the game. Consider A:= To win the game, C:= To tie the game. We know that P(A|B)=P(C|B). When the team doesn't lose, then the team either ties or wins, this means that

[tex]P(A|B)+P(C|B) = 1[/tex]

So we get that P(A|B) = P(C|B) = 1/2. Let us find P(A)

[tex]P(A|B) = \frac{P(A\cap B)}{P(B)} = \frac{P(A)}{P(B)}=\frac{1}{2}[/tex]

Then [tex]P(A) = \frac{P(B)}{2} = 0.2[/tex]. By an analogous calculation we have that P(A) = P(C) = 0.2.

We will define the following events: [tex]W_i[/tex] is the event that the team wins the game i, [tex]T_i[/tex] is the event that the team ties the game i and [tex]L_i[/tex] is the event that the team loses the game i. In this notation, we have that

[tex]P(W_1) = P(T_1) = 0.2, P(L_1) = 0.6[/tex]

By reasoning the same way for the second game, we can calculate that

[tex]P(W_2)=P(T_2)=0.35, P(L_2) = 0.3[/tex]

To calculate the PMF we must check all the possible outcomes of the results of both games. Since we can either win (W), tie(T) or lose(L) a game, we will express the outcome as follows TW(3) means that the team ties  the first game and wins the second one, for a total of points. In this way, the possible outcomes are

WW(4), WT(3), WL(2), TW(3), TT(2), TL(1), LW(2), LT(1), LL(0)

We see that the number of possible points are 0,1,2,3,4. Let X be the number of points, to get the pmf of X is to give the probability P(X=k) for k=0,1,2,3,4 explicitly. Note that since each game is independent of each other, to get the probability of one of the outcomes it suffices to multiply the probability of each event. For example we have that [tex]P(WW) = P(W_1)\cdotP(W_2) = 0.07[/tex]

Then, the pmf is given by

[tex]P(X=0) = P(LL) = 0.18[/tex]

[tex]P(X=1)=P(LT)+P(TL) = 0.27[/tex]

[tex]P(X=2)=P(LW)+P(TT)+P(WL) = 0.34[/tex]

[tex]P(X=3)=P(WT)+P(TW) = 0.14[/tex]

[tex]P(X=4)=P(WW)= 0.07[/tex]


Related Questions

100 POINTS


PLEASE PROVIDE STEPS. FOR BOTH
FIND THE INTEGRALS

Answers

Answer:

8. -⅓ cos³x + C

9. sec x + eˣ + C

Step-by-step explanation:

8. ∫ sin x cos²x dx

If u = cos x, then du = -sin x dx.

∫ -u² du

-⅓ u³ + C

-⅓ cos³x + C

9. ∫ (sec x tan x + eˣ) dx

∫ sec x tan x dx + ∫ eˣ dx

These are both standard integrals:

sec x + eˣ + C

Question 8:

∫sinxcos²xdx

∫-u²du (let u = cos(x))

-∫u²du

-u(^2+1)/2+1

-cos^(2+1)(x)/2+1

-1/3cos³(x)

-1/3cos³(x) + C

Question 9:

∫(secxtanx + eˣ)dx

∫sec(x)tan(x)dx + ∫eˣdx (apply sum rule)

sec(x) + eˣ (sec(x)tan(x)dx = sec(x) and eˣdx = eˣ)

sec(x) + eˣ + C

Best of Luck!

Estimate the sum of 17.36 and 8.7 BY ROUNDNG TO THR NEAREST WHOLE NUMBER BEFORE ADDING...?

A.9

B.10

C.25

D.26

E. None correct

Answers

Answer:

D. 26

Step-by-step explanation:

We have to round to whole numbers before adding.

When approximating to whole numbers, if the number after the decimal is less than 5, you round down to 0 but if it is greater or equal to 5, you round up to 1.

17.36 ≅ 17

8.7 ≅ 9

Therefore:

17 + 9 = 26

Max wants to purchase a wall hanging. He is choosing between one shaped like a trapezoid and one shaped like a kite. He will choose the wall hanging with the greater area. Which wall hanging will Max choose?

Answers

Answer:

Max will choose the wall hanging that is shaped like a trapezoid.

Step-by-step explanation:

To find the area of the trapezoid, break it into a triangle and another trapezoid. Use the formula for the area of a triangle (A=base*height*1/2) and the formula for the area of a trapezoid (A=base+base*height*1/2). The area of the trapezoid is 672 square centimeters.

To find the area of the kite, break it into two identical triangles. (There's a horizontal line between them.) Use the formula for the area of a triangle for both, then add the two areas. The area of the kite is 648 square centimeters.

Finally, we know that 672>648. Therefore, Max will choose the wall hanging that is shaped like a trapezoid.

Hope this helps! Tell me if you have any other questions:)

Answer:trapezoid

Step-by-step explanation:

THIS IS MATH WORK AND IS VERY CONFUSING
I NEED HELP PLEASE
ASAP PLEASE
(Could you show work too thanks :D)

Answers

Step-by-step explanation:

1.

   First blank: total amount of outcomes

2.

   since there's four possible outcomes: (Head-Head, Head-Tail, Tail-Head, and Tail-Tail) Mason should expect to win 1/4 of the time, or roughly 50 times.

3.

   a) F

   b) F

   c) T

   d) T

   e) T

    f) T

4.

17/36, because 17 of the answers are greater than 10 and there are 36 total answers.

 

Sorry I didn't answer all of them, hopefully this still helps!

Goodluck with your schoolwork/homework!

--------------------------------------------------------------

Apologies in advance for any errors/bad explanations.

How do I type in exponents

Answers

Answer:

on what

Step-by-step explanation: normaly you have a button that you can have certain characters

A friendly contest involves randomly drawing a marble from a bag that contains 16 blue marbles, 12 red
marbles, and 8 yellow marbles. If a blue marble is drawn, Nathan wins. If a red marble is drawn, Taylor wins.
If a yellow marble is drawn, Cady wins.
Who is most likely to win the contest?
1 Nathan
2 Cady
3 They are equally likely to win.
4 Taylor

Answers

Answer: I have a huge feeling it would be Nathan because he has the most blue marble. Yk?

€1.4 m
1.9 m
Tim has to cover 3 tanks completely with paint.
Each tank is in the shape of a cylinder with a top and a bottom.
The tank has a diameter of 1.4 metres and a height of 1.9 m.
A tin of paint covers 5 m
Find the total surface area of the 3 tanks and state how
many tins of paint Tim will need to buy
You must show your working
Total marks 5

Answers

Answer:

Step-by-step explanation:

Since each tank is cylindrical, we would apply the formula for determining the total surface area of a cylinder which is expressed as

Total surface area = 2πr² + 2πrh

Where

r represents the height of the cylinder.

h represents the height of the cylinder.

π = 3.14

From the information given,

Height = 1.9

Diameter = 1.4

Radius = diameter/2 = 1.4/2 = 0.7

Total surface area = 2 × 3.14 × 0.7² + 2 × 3.14 × 0.7 × 1.9 = 3.0772 + 8.3524 = 11.4296 m²

Total surface area of the 3 cylinders = 11.4296 × 3 = 34.29 m²

Since a tin of paint covers 5 m², the number of tins paints that Tim will need to buy is

34.29/5 = 6.858

Since the tins of paint must be whole numbers, he needs to buy 7 tins of paints.

if you know the area How would you find the diameter of a circle?

Answers

Step-by-step explanation:

formular of area circle = pi*

[tex] {? \\ radius}^{2} [/tex]

=> radius =

[tex] \sqrt{area \div pi } [/tex]

diameter = 2* radius.hope this help

Shira packs 170 lemon bars in boxes for the bake sale. Each box holds 8 lemon bars. She takes home the lemon bars tha are leg over after she has filled as many boxes as possible. Ahora use partial quotients to find how many boxes of lemon bars she can fill to sell at the bake sale. She finds only two partial quotients when she divides. Use the numbers in the box to answer the questions
1 2 7 8 20 21 23 27 29

Answers

Question:

1. How many full boxes of lemon bars can Shira fill?

2. How many delicious lemon bars will she be taking home?

Answer:

1. Number of filled box = 21

2. Number of take home = 2

Step-by-step explanation:

Given

Number of lemon bars = 170

Each bar contains 8 lemon bars

Required

(1) & (2)

To calculate the number of boxes Shira can fill, we simply divide the total number of bars by constituents of each bar .

i.e.

Number of filled box = 170/8

Number of filled box = 21.25

But here, we only need the quotient of the division because it represents the filled boxed.

So,

Number of filled box = 21

Calculating the number of take home.

We'll follow the same steps as (1) above but here, we only need the remainder of the division.

When 170 is divided by 8, the remainder is 2.

So, number of boxes she'll take home is 2.

See calculation below

Number of take home = 170 % 8

Number of take home = 2

Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid

Answers

Answer:

93.25% probability that they have taken this steroid

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test

Event B: Taking the steroid.

Suppose the probability of an athlete taking a certain illegal steroid is 10%.

This means that [tex]P(B) = 0.1[/tex]

Given that the athlete has taken this steroid, the probability of a positive test result is 0.995.

This means that [tex]P(A|B) = 0.995[/tex]

Positive test:

99.5% of 10%(If the athlete has taken).

100-99.2 = 0.8% of 100-10 = 90%(Athlete has not taken)

Then

[tex]P(B) = 0.995*0.1 + 0.008*0.9 = 0.1067[/tex]

Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.1*0.995}{0.1067} = 0.9325[/tex]

93.25% probability that they have taken this steroid

Barnes and Nobles buys a book for $14.25. They markup the price of the book by 35%.

Answers

Answer:

$19.24

Step-by-step explanation:

Take 14.25 times 1.35.

The markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.

What is the markup rate?

The markup rate is computed by dividing a unit's gross profit (its sales price less its cost to create or buy for resale) by its cost.

Barnes and Noble buy a book for $14.25. They mark up the price of the book by 35%.

As per the question, we have

cost = $14.25

markup rate = 35% = 0.35

Let's x represent markup for the book,

markup rate = markup/sale price × 100%

35% = x / $14.25

0.35 = x / $14.25

x = $14.25 × 0.35

Apply the multiplication operation, and we get

x = 4.9875

So sale price = markup + cost

So sale price = $4.9875 + $14.25

So sale price = $19.237

Thus, the markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.

To learn about the markup rate click here:

brainly.com/question/11999225

#SPJ2

Jay earns $8 an hour when he works at his uncle’s store. He earns $9 an hour when he does yard work for his neighbor. Which expression represents the total amount he will earn in a week when he works u hours at his uncle’s store and v hours doing yard work for his neighbor?

Answers

Answer:

8u+9v

Step-by-step explanation:

Answer:

8u+9v

Step-by-step explanation:

What is the quotient?
(6 * 108) = (1.5 x 10-4)
4 x 1012
4 x 104
4 x 10-32
4 * 10-2​

Answers

Answer:

The first choice.

Step-by-step explanation:

6 * 10^8 /  1.5 * 10^-4

= (6/1.5)  * (10^(8 - (-4))

= 4 * 10^12.

Answer:

4 x 1012

Step-by-step explanation:





Consider that point A is reflected across the x-axis. What is the distance between point A and the point of its reflection?

Answers

Answer:

It would be 2 x the absolute value of the y coordinate.

Step-by-step explanation:

Example:

(5,-3)

Absolute value of y-coordinate is 3 and distance would equal 2 x 3 = 6 units apart.

Plz help
What does “|” mean in mathematical term
Thanks

Answers

Answer:

Step-by-step explanation:

If you meant " | ", as in |x|, that's "absolute value."  The domain of this function is "all real numbers," and the range is "all real numbers zero or greater."


(13 – 6)^2 (5 + 2)^2÷(5 – 2)^3

Answers

Answer:

88 25/27

Step-by-step explanation:

(13 – 6)^2 (5 + 2)^2÷(5 – 2)^3

PEMDAS

Parentheses first

(7)^2 (7)^2÷(3)^3

Then exponents

49*49 ÷27

Then multiply and divide from left to right

2401÷27

2401/27

88 25/27

88.92592593

Answer:

Step-by-step explanation:

(7)^2(7)^2 / (3)^3

49*49 / 27

2401/27

88 25/27

Consider the graph of the exponential function, y =3(2)^x. The x- intercept of the graph is

Answers

Answer:

the x intercept is 2

Step-by-step explanation:

I just went over this unit

Answer:

2

Step-by-step explanation:

Brainliest for anyone if they get this CORRECT.

Answers

answer is D7/2

hope it helps!!!!!!!!!!!!!!!!!!!!!!

There are 14math teachers and 26 science teachers at school today. What is the ratio of math teachers to math and science teachers at school?

Answers

Answer is 7:20

It's basically asking "what is the ratio of math teachers to total teachers?" assuming there are only math and science teachers at this school. For the sake of simplicity, let's just go with that. We have 14 math teachers and 14+26 = 40 teachers total. The ratio of math to total is 14:40 which reduces to 7:20 when we divide both parts of the ratio by the GCF 2.

Answer: 7: 13

The ratio would be 14: 26, however you are most likely asked to simplify it. Which is why the answer would be 7: 13

I hope this helped! :DD

What is the area of a rectangle with sides length of 5/12 feet and 2/3 feet

Answers

Answer:

The answer is 10/36 or if you want to simplify, 5/18

Step-by-step explanation:

To solve the area of a rectangle, you need to multiply the sides with each other, so 5/12 x 2/3 is 10/36 (unsimplified) . You multiply the numerators and then the denominators and simplify.

3/4 x 1/4

next problme: 3/5 x 1/5


100 pts

Answers

Answer:

0.1875 and 0.12

Step-by-step explanation:

3/4x1/4 is 0.1875. 3/5 x 1/5 is 0.12

Answer:

1)0.1875

2)0.12

Step-by-step explanation:

We conduct a study to determine whether the majority of community college students plan to vote in the next presidential election. We choose a significance level of 0.05. We survey 650 randomly selected community college students and find that 54% of them plan to vote. The P-value is 0.02. H0: 50% of community college students plan to vote in the next presidential election. Ha: More than 50% of community college students plan to vote in the next presidential election. What can we conclude

Answers

Answer:

we can conclude that more than 50% of community college students plan to vote in the next presidential election

Step-by-step explanation:

Decision Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 95% confidence interval) ---- reject Null hypothesis

Z score < Z(at 95% confidence interval) ------ accept Null hypothesis

Null hypothesis H0: 50% of community college students plan to vote in the next presidential election

H0: p = 0.50

Ha: More than 50% of community college students plan to vote in the next presidential election

Ha: p > 0.50

P-value = 0.02

From the decision rule;

Since the p-value for this study is less than the significance level.

0.02 < 0.05

So, we reject the null hypothesis, there is enough evidence to reject the null hypothesis. We thereby accept the alternative hypothesis.

Therefore, we can conclude that more than 50% of community college students plan to vote in the next presidential election

Trisomy 18 (T18) is a rare genetic disorder that severely disrupts a baby's development prior to birth. Many die before birth and most die before their first birthday. T18 occurs in only 1 in 2500 pregnancies in the U.S. A genetic test on the mother's blood can be done to test for T18 in her baby. The overall probability of a positive test result is 0.010384. The probability of a positive test result for a baby with T18 is 0.97. The probability of a negative test result for a baby without T18 is 0.99. A mother's blood tests positive for T18. What is the probability that her baby has T18

Answers

Answer:

3.74% probability that her baby has T18

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test.

Event B: The baby having T18.

T18 occurs in only 1 in 2500 pregnancies in the U.S.

This means that [tex]P(B) = \frac{1}{2500} = 0.0004[/tex]

The probability of a positive test result for a baby with T18 is 0.97.

This means that [tex]P(A|B) = 0.97[/tex]

The overall probability of a positive test result is 0.010384.

This means that [tex]P(A) = 0.010384[/tex]

What is the probability that her baby has T18

[tex]P(B|A) = \frac{0.0004*0.97}{0.010384} = 0.0374[/tex]

3.74% probability that her baby has T18

j+ 12 =25 find the solution to equation algebtaically​

Answers

Answer:

j= 13

just subtract 12 from 25

Start by isolating the j.

Subtract 12 from both sides.

On the left, the 12 and -12 cancel.

On the right, 25 - 12 is 13.

So we have j = 13.

The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tower. The height, h, of the penny is recorded after each second, t, in the table. Write an equation for the curve of best fit, then find the approximate height of the penny after 7 seconds.

Answers

Answer:

The equation for the height of the penny in function of time is:

[tex]h(t)=1451-16t^2[/tex]

After 7 seconds, the penny will be at a height of 667 feet.

Step-by-step explanation:

The penny will have a free fall.

The initial velocity is zero, and the initial height is h(0)=1,451.

The acceleration will be the gravity, that has a value g=32 ft/s^2.

Then, we can model this starting by the speed:

[tex]dv/dt=-g\\\\v(t)=v_0-gt=-gt[/tex]

Then, the height becomes:

[tex]dh/dt=v(t)=-gt\\\\h(t)=h_0-\dfrac{gt^2}{2}=1451-\dfrac{32}{2}t^2\\\\\\h(t)=1451-16t^2[/tex]

The approximate height of the penny after 7 seconds can be calculated as:

[tex]h(7)=1451-16(7^2)=1451-16*49=1451-784=667[/tex]

After 7 seconds, the penny will be at a height of 667 feet.

What is the fractionation of X2 - 6X + 5

Answers

Answer:

  (x -1)(x -5)

Step-by-step explanation:

We recognize that 6 is the sum of the factors of 1·5, so we can write the factorization as ...

  x^2 -6x +5 = (x -1)(x -5)

_____

The product of factors will be ...

  (x +a)(x +b) = x^2 +(a+b)x +ab

So, the binomial constants "a" and "b" are factors of the trinomial constant that have a sum equal to the coefficient of the linear term. Here, those are factors of +5 that have a sum of -6. The factors of interest are -1 and -5: 5 = (-1)(-5); -6 = (-1) +(-5).

how many thousands make 5crore​

Answers

Answer:

50,000 thousands make a crore.

Step-by-step explanation:

One crore (1,00,00,000) is equal to one hundred lakh (10,000 × 1,000). Thus, 10,000 thousands make a crore.

When Jonas becomes the Receiver of Memory, he gets a rule that he may not tell his dreams. He wants to know how many of his 505050 classmates have the same rule. He asks 555 friends from his class whether they may tell their dreams. Of those, 444 say that they may.

Answers

Answer:

101010 classmates can't tell their dreams.

Step-by-step explanation:

I'm not sure what the question is, but if it is an average thing than 444 of 555 is 80 percent, so if that is what it wants 404040 of the students can share their dreams, and 101010 can't.

Hope this helps!

g(t) = 6t - 1

g ( ) = -7

Answers

Answer:

  g(-1) = -7

Step-by-step explanation:

Put the given value for g(t) into the first equation and solve for t.

  -7 = 6t -1

  -6 = 6t . . . . . . add 1

  -1 = t . . . . . . . . divide by 6

g(-1) = -7

Answer: -1

Step-by-step explanation:

What is the length of AC? PLEASE HELP ASAP WILL GIVE BRAINLIEST TY

Answers

Answer:

2.33 units

Step-by-step explanation:

[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]

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