Question

The probability that Shelly will go to a movie (event

a. on Friday is 0.78, and the probability that Danielle will go to a movie (event
b. the same day is 0.63. The probability that Shelly will go to a movie, given that Danielle goes to a movie, is 0.87. Which statement is true?

Answer 1

P(A|B) says it's the probability of A given B has already occured. If they are independent, it shouldnt matter if B occured or not so if they were independent P(A|B) = P(A) but they dont, so dependent

Answer 2

Explanation:

Let A be the event that Shelly will go to a movie on Friday and B the event hat Danielle will go to a movie

P(A) = 0.78 and P(B) = 0.63

P(A/B) = 0.87

P(A/B) =
`(P(AB))/(P(B)) =0.87`

Hence

`P(AB) = 0.87*0.63`

P(AB) ≠P(A)P(B)

Hence A and B are not independent.

A and B are dependent.