Question

Armonte of Salsa Verde Inc. hired Jocelyn; creator of the stats rap: “Hu Ghives Ah Factorial!” to help him find the following. (Why she was hired, is a mystery!)

a) P (A and W), when P (A) = .6467 and P (W given A) = .1959.

b) P(Logs | Women), when P(Women) = .40 and P(Women and Logs) = .10

c) P(X or Q), given P(X) = 0.82, P(Q) = 0.52 and P(X and Q) = 0.49

Answer 1

a)

P (A) = .6467 and P (W given A) = .1959

Baye's theorem:

P (W given A) = P (A and W) /  P (A)

P (A and W), = P (W given A) *   P (A)

= .1959 * .6467 = 0.1267

b)

P(Women) = .40 and P(Women and Logs) = .10

P(Logs | Women) = P(Women and Logs) /  P(Women)

= .10/.40 = .25

c)

P(X or Q), given P(X) = 0.82, P(Q) = 0.52 and P(X and Q) = 0.49

P(X or Q) = P(X) + P(Q) - P(X and Q)

= 0.82 + 0.52 - 0.49

= .85

Please revert back in case of any doubt.

Please upvote. Thanks in advance.