Question

Suppose that we have two events, A and B, with P(A) = 0.50,P(B) = 0.60,and P(A ∩ B) = 0.20.

(a)Find P(A | B). (Round your answer to four decimal places.)
P(A | B) = ?
(b)Find P(B | A).
P(B | A) = ?
(c)Are A and B independent? Why or why not?
A and B ---Select--- (are, are not) independent because ---Select--- (PA | B) = P(A) .P(A | B) ≠ P(B) ,P(A | B) ≠ P(A) P(A | B) = P(B) .)

Answer 1

To find P(A | B), divide P(A ∩ B) by P(B). To find P(B | A), divide P(A ∩ B) by P(A). A and B are not independent because P(A | B) is not equal to P(A) or P(B).

Step-by-step explanation:

To find P(A | B), we can use the formula P(A | B) = P(A ∩ B) / P(B). Plugging in the given values, we have P(A | B) = 0.20 / 0.60 = 0.3333.

To find P(B | A), we can also use the formula P(B | A) = P(A ∩ B) / P(A). Plugging in the given values, we have P(B | A) = 0.20 / 0.50 = 0.4.

A and B are not independent because P(A | B) = 0.3333 which is not equal to P(A) = 0.50 or P(B) = 0.60.