Can somebody help me with these. with solution

1 Two balls are drawn in succession without replacement from a box containing 4 red balls and 3 black balls. Let Y be the random variable, where Y is the number of the red balls. What is the expected value of this random event?

2. Two balls are drawn in succession from a box without repetition containing 3 red 3 blue and four yellow marbles. What is the probability that they are of the same color?

Answers

Answer 1

Answer:

See below, please.

Explanation:

Part 1.

Let Y be the random variable representing the number of red balls drawn in succession. The possible outcomes are (R, R), (R, B), (B, R), and (B, B). We can calculate the probability of each outcome as follows

P(Y=0) = P(B, B) = (3/7) * (2/6) = 1/7

P(Y=1) = P(R, B) + P(B, R) = (4/7) * (3/6) + (3/7) * (4/6) = 12/42 + 12/42 = 24/42

P(Y=2) = P(R, R) = (4/7) * (3/6) = 2/7

The expected value of Y is given by:

E(Y) = Σ yi * P(Y=y)

= 0 * (1/7) + 1 * (24/42) + 2 * (2/7)

= 0 + 8/14 + 4/7

= 16/14

= 1.14

Therefore, the expected value of Y is 1.14.

Part 2.

The total number of ways to draw two marbles from the box is 10C2 = 45. The number of ways to draw two marbles of the same color is 3C2 + 4C2 = 3 + 6 = 9. Therefore, the probability of drawing two marbles of the same color is

P(same color) = 9/45 = 1/5

Therefore, the probability that the two balls are of the same color is 1/5.

Related Questions

formal letter to step down in position

Answers

[Your Name]

[Your Address]

[City, State ZIP Code]

[Your Email]

[Date]

[Recipient Name]

[Recipient Position]

[Company Name]

[Address]

[City, State ZIP Code]

Dear [Recipient Name],

I am writing this letter to inform you that I have decided to step down from my position as [Your Position] at [Company Name]. My resignation is effective from [Date].

I have made this decision after much consideration and reflection on my personal and professional goals. While I have greatly enjoyed working at [Company Name] and appreciate the opportunities and support provided by the organization, I have decided that it is time for me to pursue other career opportunities.

I will ensure a smooth transition by completing my pending work and helping my replacement to settle into the role. I am willing to assist in any way possible to ensure that my duties and responsibilities are transferred smoothly to my successor.

I would like to take this opportunity to express my gratitude to [Recipient Name] and the entire management team for their support, guidance, and mentorship during my time at [Company Name]. I have learned a lot from my colleagues, and I am grateful for the professional growth opportunities provided to me.

Please let me know if there is any additional information you need from me or if I can assist in any way during this transition period.

Thank you for understanding my decision.

Sincerely,

[Your Name]

What is the guidance system of a car?

Answers

Answer:

Parking Guidance Systems (PGS) are a form of technology that is designed for drivers providing them with real time parking information. A PGS is an advanced form of Car Counting or vehicle detection technology that provides dynamic data to facilitate vehicle circulation within a car park.

All of the following are common manual transmission problems EXCEPT: (A) bent shift mechanism. B) worn thrust washers. (C) clogged modulator valve. (D) damaged extension housing.

Answers

Option (C) clogged modulator valve is not a common manual transmission problem. This component is typically associated with automatic transmissions, not manual transmissions.

Explanation

Manual transmission problems can include a range of issues that can affect the performance of the transmission. Here short explanation about other option except C as common manual transmission problems:

Bent shift mechanism.
The shift mechanism in a manual transmission is responsible for moving the gears into the correct position for each gear change. If the shift mechanism is bent or damaged, it can cause difficulty in shifting gears or even prevent the transmission from shifting at all. This can happen due to wear and tear, damage from impact or other causes.Worn thrust washers.
Thrust washers are small components in the transmission that help to control the movement of the gears. If the thrust washers become worn, they can cause excessive play in the gears, leading to difficulty in shifting and even gear slippage. This can happen due to normal wear and tear or improper lubrication.Damaged extension housing.
The extension housing is the outermost component of the transmission on the backside that houses the output shaft. If it becomes damaged due to wear and tear, impact or other causes, it can cause leaks in the transmission or even prevent it from operating altogether. A damaged extension housing can cause the transmission to fail or operate poorly.

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Fill in the Blank
Complete the sentence.
modeling is
a design for the underlying shape to represent exterior surfaces that includes shapes and curvatures.

Answers

The completed sentence is: Modeling in computer-aided design (CAD) is a design for the underlying shape to represent exterior surfaces that includes shapes and curvatures.

What is computer aided design and how is it important to modelling?

Computer-aided design (CAD) is the use of computer software to create, modify, analyze, and optimize designs for a wide range of industries and applications. CAD software is used by engineers, architects, designers, and manufacturers to create 2D and 3D models, drawings, and simulations of products, buildings, and structures.

CAD is important to modelling because it allows designers to create highly accurate and detailed representations of their designs, which can be easily modified, tested, and optimized before production.

This can save time and money by reducing errors and minimizing the need for physical prototypes. CAD also enables collaboration among team members and stakeholders, and facilitates the integration of design data into other stages of the product development process.

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how many grams of water can be heated from 10 degrees to 45 degrees using 20,500 joules of energy

Answers

Therefore, 20,500 Joules of energy can heat 1,104.3 grams of water from 10 degrees Celsius to 45 degrees Celsius.

Specific heat capacity

Calculate the energy (in Joules) required to heat 1 gram of water from 10 degrees Celsius to 45 degrees Celsius:

Q = m * c * ΔT

Q = 1 gram * 4.184 Joules/gram-degree Celsius * (45 - 10) degrees Celsius

Q = 18.47 Joules

Calculate the amount of water (in grams) that can be heated with 20,500 Joules of energy:

20,500 Joules / 18.47 Joules = 1,104.3 grams

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what is the ampere unit of force and how is that unit derived?

Answers

The ampere (/aempr/, US: /mpr/; symbol: A), also known as the amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to one coulomb, or 6.2415090741018 electrons passing through a point in one second.

What is ampere?

The ampere, commonly abbreviated as "amp," is the base unit of electric flow in the International System of Units (SI). It was named after French mathematician and physicist André-Marie Ampère (1775-1836), widely regarded as the father of electrodynamics. The ampere is defined by the International System of Units in terms of other base units by estimating the electromagnetic power between electrical conductors that carry the electric flow. The previous CGS estimation framework employed two distinct definitions of current, one based on SI units and the other on electric charge as the base unit. The charge unit is calculated by measuring the power between two charged metal plates. The ampere was then defined as one coulomb of charge per second. SI defines the coulomb as the unit of charge.

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