The television network MTV airs a show called “Are You The One?” Unlike many oth

Question

The television network MTV airs a show called “Are You The One?” Unlike many other TV shows on the network, the show features a surprising amount of mathematics. 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.
In season 5, the producers decided to increase the cast to 22 people, forming 11 perfect matches. How would this affect the group’s chance of winning? If the number of players is 2n, what happens to the probability of the group winning as n ? What happens to the probability of a blackout as n ?
The television network MTV airs a show called “Are You The One?” Unlike many other TV shows on the network, the show features a surprising amount of mathematics. 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.
In season 5, the producers decided to increase the cast to 22 people, forming 11 perfect matches. How would this affect the group’s chance of winning? If the number of players is 2n, what happens to the probability of the group winning as n ? What happens to the probability of a blackout as n ?
The television network MTV airs a show called “Are You The One?” Unlike many other TV shows on the network, the show features a surprising amount of mathematics. 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.
In season 5, the producers decided to increase the cast to 22 people, forming 11 perfect matches. How would this affect the group’s chance of winning? If the number of players is 2n, what happens to the probability of the group winning as n ? What happens to the probability of a blackout as n ?

Explanation / Answer

Chance of winning would be 1/11! = 1/39916800

Chance of winning would reduce to 1/11 the original chance.

As n tends to infinity, probability will reduce to 0

Possibility of blackout = 1/n .

as N tends to infinity, possibility of blackout will also reduce to 0

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