The San Francisco football team plays better in fair weather. They have a 70% chance of winning in good weather but only a 20% chance of winning in bad weather. (a) If they play in the Super Bowl in Wisconsin and the weatherman predicts a 60% chance of snow that day, what is the probability that San Francisco will win. (b) Given that San Francisco lost, what is the probability that the weather was bad

a) 40% probability that San Francisco will win.

b) 80% probability that the weather was bad

Step-by-step explanation:

In this problem, there are these following probabilities:

60% probability of bad weather.

If there is bad weather, 20% probability of SF winning.

100-60 = 40% chance of good weather.

If there is good weather, 70% probability of SF winning.

(a) If they play in the Super Bowl in Wisconsin and the weatherman predicts a 60% chance of snow that day, what is the probability that San Francisco will win.

If it snows, 20% probability of winning. If it does not snow, 70% probability of winning.

0.2*0.6 + 0.7*0.4 = 0.4

40% probability that San Francisco will win.

b) Given that San Francisco lost, what is the probability that the weather was bad:

Conditional probability:

We use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: SF losing

Event B: Bad weather

P(A):

Probability of SF losing, which from a), is 0.6 = 60%.

P(A and B)

60% chance of snow. If it snows, 80% probability of SF losing. So

Then

80% probability that the weather was bad

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation:

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (