Answer to Question #91644 in Statistics and Probability for Sibel Gercek

Question

For married couples living in a certain suburb, the probability that thehusband will vote on a bond referendum is 0:24, the probability that the wife willvote on the referendum is 0:16, and the probability that both the husband and thewife will vote is 0:12. What is the probability that
a) a randomly selected married couple willnotvote?
b) a wife will vote, given that her husband will vote?
c) a husband will vote, given that his wife willnotvote?

Answer 1

b) P(A | B) = P(A, B) / p(B). P(wife | husband) = 0.12 / 0.24 = 0.5

a)

P(NOT wife & NOT Husband) = 1 - P(wife & Husband) - P(wife & NOT Husband) - P(NOT wife & Husband) =

= 1 - P(wife & Husband) - P( NOT Husband | wife) * P(wife) - P(NOT wife | Husband) * P(Husband) =

= 1 - P(wife & Husband) - ( (1 - P( Husband | wife)) * P(wife) ) - ( (1 - P( wife | Husband)) * P(Husband) ) =

= 1 - P(wife & Husband) - P(wife) - P(Husband) + 2 P(wife & Husband) =

= 1 + P(wife & Husband) - P(wife) - P(Husband) =

= 1 + 0.12 - 0.24 - 0.16 = 0.72

c)

P(husband | NOT wife) = 1 - P(NOT husband | NOT wife).

P(NOT husband | NOT wife) = P(NOT husband & NOT wife) / P(NOT wife)

P(NOT husband | NOT wife) = 0.72 / 0.84

P(husband | NOT wife) = 1 - 0.72 / 0.84 = 0.1429

ANSWER:

a) 0.72

b) 0.5

c) 0.143