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?
a. Events A and B are independent because P(A|B) ≠ P(A).
b. Events A and B are independent because P(A|B) = P(B).
c. Events A and B are dependent because P(A|B) = P(A) x P(B).
d. Events A and B are dependent because P(A|B) ≠ P(A).
e. Events A and B are dependent because P(A|B) = P(A).

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?
a. Events A and B are independent because P(A|B) ≠   P(A).
b. Events A and B are independent because P(A|B) = P(B).
c. Events A and B are dependent because P(A|B) = P(A)  x  P(B).
d. Events A and B are dependent because P(A|B) ≠   P(A).
e. Events A and B are dependent because P(A|B) = P(A).

xenesis98 · Answer

how

satellite73 · Answer

A doesn't even make sense 
if they are unequal, they are dependent, not independent

satellite73 · Answer

if the events are independent, then $$P(A)\times P(B)=P(A\cap B)$$

satellite73 · Answer

if not, they are dependent

bmk614 · Answer

It is B. They are independent and they have to equal each other, because not equaling it would be dependent.