The television network MTV airs a show called “Are You The One?”The premise of t

Question

The television network MTV airs a show called “Are You The One?”The premise of the show is that ten men and ten women live in a house together. Secretly, the group has been split into ten“ correct” male-female pairs which a matchmaker believes to be especially compatible. In other words, each player has exactly one “perfect match” of the opposite sex, though they have no idea which other player is their perfect match. A matchup ceremony happens at the end of each episode, in which the group of twenty players partition themselves into ten male-female pairs. The group wins if they get all ten pairs right at a single matchup ceremony.

1. Occasionally, the group has the ability to use a truth booth, which can take a single pair and answer denitively whether they are a perfect match or not. What is the conditional probability of a perfect matchup ceremony, conditioned on the event that the truth booth conrms that the couple selected was a perfect match, and that couple chooses to be paired at the next matchup ceremony

Explanation / Answer

We now know that one pair is correct as it is given that single pair knows the perfect match, now we just need to find the probability that other four couples pair up correctly

i.e =P(first partner choses his perfect match amoung 4 people)*P(second partner choses his perfect match amoung 3 other people)*P(third partner choses his perfect match amoung 2 people)*P(last partner choses his perfect match amoung remaining last person)

=1/4*1/3*1/2*1

=1/24

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