5. +-110 points My Note Maria and Thomas are part of a group of 4 women and 8 me

Question

5. +-110 points My Note Maria and Thomas are part of a group of 4 women and 8 men who will participate in a chess tournament. The 12 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

answer

(a) Maria has 11 different possible opponents. So the probability that will be Thomas is 1/11.
(b) 11 different opponents, 3 are women. so the prob her opponent is a woman is 3/11.
(c) First Maria chooses her opponent, 3/11 prob it is a woman. If that happens, then when Thomas chooses his opponent, there are 9 people left, of whom 7 are men. So prob is 3/11 x 7/9
(d) same as (c), except Thomas has 7/9 prob of choosing a woman.

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