Question

Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is 0.02, the probability that "she's up all night for good fun" is 0.27, and the probability that "she's up all night 'til the sun" is 0.29, what's the probability that "she's up all night 'til the sun" AND "she's up all night for good fun"?

Answer 1

0.54

Explanation:

A = "she's up all night 'til the sun"

B = "she's up all night for good fun"

P(A) = 0.29

P(B) = 0.27

P(A or B) = 0.02

The following relationship is known:

`P(A\ or\ B) = P(A)+P(B) - P(A\ and\ B)`

Therefore, applying the given data:

`P(A\ and\ B) = P(A)+P(B)-P(A\ or\ B)\\P(A\ and\ B) = 0.29+0.27-0.02\\P(A\ and\ B) = 0.54`

The probability that "she's up all night 'til the sun" AND "she's up all night for good fun" is 0.54.