1. Consider rolling a fair 6-faced die twice. Let A be the event that the sum of

Question

1. Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is equal to 7, and B be the event that the first one is an odd number.

(a)   What is the probability that the sum of the two rolls is equal to 7 given that the first one is an odd number? Show all work. Just the answer, without supporting work, will receive no credit.

(b)   Are event A and event B independent? Explain.

2. Answer the following two questions.

a. UNLV Stat Club is sending a delegate of 2 members to attend the 2018 Joint Statistical Meeting in Vancouver. There are 10 qualified candidates. How many different ways can the delegate be selected?

b. A bike courier needs to make deliveries at 5 different locations. How many different routes can he take?

3. Imagine you are in a game show. There are 20 prizes hidden on a game board with 100 spaces.

One prize is worth $50, nine are worth $20, and another ten are worth $10. You have to pay $5 to the host if your choice is not correct. Let the random variable x be the money you get or lose.

a. Complete the following probability distribution

X

P(x)

-$5

$10

$20

$50

b. What is your expected winning or loss in this game? Be specific in your answer whether it’s winning or loss.

3. Mimi joined UNLV basketball team in spring 2017. On average, she is able to score 20% of the field goals. Assume she tries 10 field goals in a game.

a. Let X be the number of field goals that Mimi scores in the game. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

b. Find the probability that Mimi scores at least 3 of the 10 field goals. (round the answer to 3 decimal places)

X

P(x)

-$5

$10

$20

$50

Explanation / Answer

Question 1:

A: The sum of 7 could be obtained here as:

1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1

Therefore there are 6 ways out of the 36 combinations where the sum of 7 could be obtained.

Now the first digit could be even and odd with equal probability, therefore P(B) = 0.5 that is probability to get an odd number on the first dice throw.

Also, now the probability that the first is odd number and the sum is 7 that is:

A and B: 1 + 6, 3 + 4, 5 + 2

Therefore there are only 3 ways that this could be achieved.

P(A and B) = 3 / 36 = (1/12 )

Now the required probability that given the first one is an odd number, the probability that the sum of the two rolls is equal to 7 is computed using bayes theorem as:

P( A | B) = P(A and B) / P(B) = (1/12) / 0.5 = 1/6

Therefore 1.6 = 0.1667 is the required probability here.

b) Here from the previous computations we saw that:

P(A and B) = (1/12)

Also, P(A)P(B) = (1/6)*0.5 = (1/12) which is equal to P(A and B)

Therefore Yes A and B are independent events.

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