Consider the following.
P(A) = 0.31 and P(B) = 0.41, and P(A and B) = 0.1271
(a) What is P(A | B)? (Give your answer correct to two decimal places.)
(b) What is P(B | A)? (Give your answer correct to two decimal places.)
(c) Are A and B independent?
yes no cannot be determined
To solve this problem, we will use the conditional probability formula:
P(A | B) = P(A and B) / P(B)
(a) To find P(A | B), plug in the values we have:
P(A | B) = 0.1271 / 0.41
P(A | B) ≈ 0.31
Therefore, P(A | B) is approximately 0.31.
(b) To find P(B | A), we can use the same formula and rearrange it:
P(B | A) = P(A and B) / P(A)
P(B | A) = 0.1271 / 0.31
P(B | A) ≈ 0.41
Therefore, P(B | A) is approximately 0.41.
(c) To determine if A and B are independent, we need to compare P(A | B) with the unconditional probability P(A). If P(A | B) is equal to P(A), then A and B are independent events. If P(A | B) ≠ P(A), then A and B are dependent events.
Here, P(A | B) = 0.31 and P(A) = 0.31, which means they are equal. Therefore, A and B are independent events.