Question

If it snows on game day there is a 32% chance the Jets will win. If it does not snow on game day there is a 41% chance the jets will win. There is a 29% chance that it will snow on game day.

a. What is the probability the Jets will win?

b. What is the probability that it snows on game day and the Jets win?

c. What is the probability that it snows on game day given that the Jets win?

Answer 1

To find the probability the Jets will win, we use the Law of Total Probability. The probability that it snows on game day and the Jets win is found using the definition of conditional probability. Lastly, to find the probability that it snows on game day given that the Jets win, Bayes' theorem is used.

Step-by-step explanation:

To solve this problem, we can use the concept of conditional probability. Let's define the following events:

A = it snows on game day

B = the Jets win

We are given:

P(B|A) = 0.32 (the probability of the Jets winning if it snows)

P(B|A') = 0.41 (the probability of the Jets winning if it doesn't snow)

P(A) = 0.29 (the probability of it snowing on game day)

a.

To find the probability of the Jets winning, we can use the Law of Total Probability:

P(B) = P(B|A)P(A) + P(B|A')P(A')

P(B) = 0.32 * 0.29 + 0.41 * (1 - 0.29)

P(B) = 0.0928 + 0.1059

P(B) ≈ 0.1987

b.

To find the probability that it snows on game day and the Jets win, we can use the definition of conditional probability:

P(A and B) = P(A) * P(B|A)

P(A and B) = 0.29 * 0.32

P(A and B) ≈ 0.0928

c.

To find the probability that it snows on game day given that the Jets win, we can use Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(A|B) = (0.32 * 0.29) / 0.1987

P(A|B) ≈ 0.4643

Answer 2

a) It is Win with snowfall OR Win without snowfall = 32% + 41% = 73% b) It is Snowfall on game day AND Win = 29% * 32% = 9.28% c) It is 32% * 29% / 73% = 12.71 %