Statistics and Probability Answers

Consider the experiment of throwing a pair of dice. We are interested in the sum of the two numbers that occur. We know that X can assume the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

1) What is the probability mass function of X?

2) What is the probability that the number of dots will be at least 4 and at most 7?

3) Find the probability that the sum will be at least 7.

Suppose that a couple in planning 3 children is primarily interested in the number of boys.

1) - Define the random variable X.

2) - What is the range of X?

3) - Find the probability function of X.

4) - Find the probability mass function

5) - Draw the graph for the probability mass function

Suppose that a pair of fair dice is thrown 1 time. Let the random variable X be the absolute difference of the dots that appear.

1) - What are the possible values of X?

2) - What is the sample space?

3) - Find the probability functions of X.

4) - Find the probability mass function

5) - Draw the graph for the probability mass function

In an experiment of rolling a balanced die twice, let X be the maximum of the two numbers obtained.

1) What are the possible values of X?

2) Write down the sample space

3) Wat is the probability function for X?

4) Determine and sketch the probability mass function of X.

5) Find the expected value of X.

6) Find the variance of X.

A contractor has submitted bids for two state construction projects. The probability that he will be awarded any contract is 0.3 and it is the same for each of the two contracts.

1) - What is the probability that he will be awarded both contracts?

2) - What is the probability that he will be awarded neither contract?

In a class, 70% of all students are boys and the rest are girls.

• 10% of the girls are smokers

• 20% of the boys are smokers

1) Find the probability that a randomly selected student is a smoker.

A survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs done in their homes. The survey also showed that 5% of the consumers were dissatisfied and had specifically complained about work by Plumber X. Plumber X does 40% of the plumbing jobs in the community.

1. What is the probability that a randomly selected consumer in this community will obtain an unsatisfactory plumbing job, given that Plumber X did the work?

2. What is the probability that a randomly selected consumer in this will obtain a  

satisfactory plumbing job, given that Plumber X did the work?

We roll a pair of dice once and are given that the two numbers that occur are not the same. Compute the following probabilities:

• i) the sum is 7

• ii) the sum is 4

• iii) the sum is 12

A commuter passes through three traffic lights on the way to work. Each light is either red, yellow, or green. An experiment consists of observing the colour of the three lights.

• i) List the 27 possible outcomes in the sample space.

• ii) Let A be the event that all the colours are the same. List the outcomes of A.

• iii) Let B be the event that all the colours are different. List the outcomes of B.

• iv) Let C be the event that at least two lights are green. List the outcomes of C.

• v) List the outcomes in 𝐴 ⋂ 𝐶.

• vi) List the outcomes in 𝐴 ⋃ 𝐵.

• vii) List the outcomes in 𝐴 ⋂ 𝐶' .

• viii) List the outcomes in 𝐴' ⋂ 𝐶 .

• ix) Are events A and C mutually exclusive? Explain.

• x) Are events B and C mutually exclusive? Explain.

There are 9 eggs out of which 4 are bad. 3 eggs are chosen at random.

1) In how many ways can we choose the 3 eggs from among the 9 eggs?

2) In how many ways can we choose 3 good eggs?

3) What is the probability that all selected eggs are good?

4) In how many ways can we choose 3 bad eggs?

5) What is the probability that all 3 selected eggs are bad ones?

6) What is the number of pairs of good eggs?

7) In how many ways can we choose 3 eggs out of which 1 is bad?

8) What is the probability that exactly one egg is bad?

9) What is the probability that at least one egg is bad?