Question

Suppose you're on vacation. The probability that it is March and you're on vacation is 5%. What is the probability that you're on vacation given that the month is March?

Answer 1

60%

Explanation:

If two events, A and B, are dependent, the probability of both occurring is: P(A and B) = P(A)·P(B|A).

Thus, the formula for conditional probability is: P(B|A) =

P(A and B)

P(A)

12 months →

1

12

= 0.0833

P(B|A) =

P(A and B)

P(A)

=

0.05

0.0833

= 0.60 → 60%

Answer 2

Follow the formula given below.

P(Mar and Vacation) = P(vacation l march) x P(March)

So it was given above that 5% is the probability that it is March and someone's vacation.

0.05 = P(vacation l march) x ( 1/12)
1 0.05
P(vacation l march)= ------- x --------
12 1

P(vacation l march) = 0.6

So the answer is 60% probability that you will have a vacation given that the month is March.