My Notes Ask Your Teacher Maria and Thomas are part of a group of 12 women and 8

Question

My Notes Ask Your Teacher Maria and Thomas are part of a group of 12 women and 8 men who will participate in a chess tournament. The 20 players will be randomly paired up into groups of two. (a) What is the probability that Maria and Thomas will be paired together? (b) What is the probability that Maria will be paired with another Woman? (c) What is the probability that Maria will be paired with another woman and Thomas will be paired with another with a man? (d) What is the probability that both Maria and Thomas are paired with a woman?

Explanation / Answer

a) Maria has 19 different possible opponents . So the probability that will be Thomas is 1/19.

b) 19 different opponents , 11 are women. so the probability that her opponent is a women is 9/19.

c) first Maria chooses her opponent, 11/19 probability it is a woman. If that happens , then when Thomas chooses his opponent , there are 17 people left , of whom 7 are men so probability is 9/ 19 * 7/17.

d) same as c) except Thomas has 10/17 probability of choosing a woman.

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