Question

Suppose that 90% of days are sunny in Los Angeles. When it's sunny, the probability that I bike to work is 75%. When it's not sunny, the probability that I bike to work is 25%. When I don't bike to work, I drive to work. If, on a randomly selected day, I am driving to work, what is the probability that it's a sunny day?

Answer 1

Answer:

75%

Step-by-step explanation:

Probability of a day being sunny (P(S)) = 0.9

Probability of driving when sunny (P(Ds)) = 1-0.75 = 0.25

Probability of a day NOT being sunny (P(N) = 1- 0.9 = 0.1

Probability of driving when sunny (P(Dn)) = 1-0.25 = 0.75

The probability of a day being sunny given that the person is driving (S) is defined as the ratio between the probability of the person driving and the day being sunny by the probability of the person driving:

$S =\frac{P(S \cap Ds)}{P(S \cap Ds)+P(N \cap Dn)} \\S=\frac{0.9*0.25}{0.9*0.25 +0.1*0.75}\\S=0.75$

There is a 75% probability that it's a sunny day.