A particular state has elected both a governor and senator. Let A be the event t

Question

A particular state has elected both a governor and senator. Let A be the event that a randomly selected voter has a favorable view of a certain party;s senator, and let B be the corresponding event for a party's governor. P(A') = 0.44 P(B') = 0.57 P(A union B) = 0.68

P(A) = 0.56 P(B) = 0.43 P(A intersect B) = 0.31

a.) What is the probability that a randomly selected voter has a favorable view of both candidates?

b.) What is the probability that a randomly selected voter has a favorable view of exactly one of these candidates?

c.) What is the probability that a randomly selected voter has an unfavorable view of at least one of these candidates?

Explanation / Answer

Ans;

a)P(A or B)=P(A)+P(B)-P(A and B)

P(voter has favorable view of both candidates)=P(A and B)=P(A)+P(B)-P(A or B)

=0.56+0.43-0.68

=0.31

b)P(exactly one of A or B occurs)=P(A)+P(B)-2P(A or B)=0.56+0.43-2*0.31=0.37

c)P(atleast one of these candidates)=P(A or B)=0.68

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