Answer :
Answer:
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
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] 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
[tex]P(A \cap B) = 0.6*0.8 = 0.48[/tex]
Then
[tex]P(B|A) = \frac{0.48}{0.60} = 0.8[/tex]
80% probability that the weather was bad