The probability of event A, given that event B has occurred, can be found using Bayes' Theorem. P(A) P(BIA) P(A) • P(BIA) + P (A') .P (BIA) Use Bayes' Theorem to find P(AIB) using the probabilities shown below. P(A) = 68%, P (A') = 32%, P (B|A) = 43%, and P (B|A') = 53% P(A/B) = ... The probability of event A, given that event B has occurred, is (Round to three decimal places as needed.)

A company has seven applicants for two positions: three women and four men. Suppose that the seven applicants are equally qualified and that no preference is given for choosing either gender. Let x equal the number of women chosen to fill the two positions. (a) Write the formula for p(x), the probability distribution of x. CAC. 3 X 2- X c²2 p(x): = p(x) = p(x): = p(x): = 4 X 2 - X mean = c³c. CAC 3 C² C p(x): = variance = X 2- X c²72 4 X 2 - x C³ C. X 4 2- X c²72 for x = 0, 1, 2 for x = = 0, 1, 2, 3, 4, 5, 6, 7 for x = 0, 1, 2, 3, 4, 5, 6, 7 for x = = 0, 1, 2 for x = (b) What are the mean and variance of this distribution? (Round your mean to one decimal place and your variance to two decimal places.) = 0, 1, 2

Given that P(A)P(A) = 0.62, P(B)P(B) = 0.27, and P(A∣B)P(A∣B) = 0.22, find the probabilities:P(B∣A)P(B∣A) = P(∼A)P(∼A) = P(∼B)P(∼B) = P(∼A∣B)P(∼A∣B) = P(∼B∣A)P(∼B∣A) = P(A∣∼B)P(A∣∼B) = P(B∣∼A)P(B∣∼A) =

E and F are mutually exclusive events. P (E) = 0.91; P(F) =0.42 . Find P (E| F )