In a television game show, contestants are asked to match babypictures of three

Question

In a television game show, contestants are asked to match babypictures of three celebrities with their respective adult pictures. Suppose a contestantmatches the pictures at random. a.what is the probability that all the pictures match? b.what is the probability that none of the picturesmatch? In a television game show, contestants are asked to match babypictures of three celebrities with their respective adult pictures. Suppose a contestantmatches the pictures at random. a.what is the probability that all the pictures match? b.what is the probability that none of the picturesmatch?

Explanation / Answer

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Allthe pictures can be rearranged in 3! Ways=6

LetP(x) denotes probability that x pictures match

Weknow that only one arrangement is correct so=1

Probability that all match = P(3) = Total correct arrangements /Ways of rearranging

= 1/6

Probability that none match=P(0)=1 – (P(1)+P(2)+P(3))

Probability that one match=P(1)= 1/3

Probability that two match=P(2)=(One matched)+(One match inremaining two)=1/3+1/2=1/6

SoP(0)=1 – (P(1)+P(2)+P(3))

=1-(1/6+1/3+1/6)

=1-(4/6)

=1-2/3

=1/3

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