Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm\'s public relations off

Question

Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm's public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness, the choice will be made by drawing two names from a hat. (This is an SRS of size 2.)
In order to find the sample space you should write down all possible choices of two of the five names.
8. How many pairs are there in the sample space?

9. What is the probability that Mei-Ling is chosen?

10. What is the probability that neither of the two men (Sam and Roberto) is chosen?

Explanation / Answer

The easiest but most tedious way to get your answer goes as follows: Write down all possible pairs of names. You can do this systematically, starting off with 1 person and pairing it up with all others and then move on with the next person. Counting these will give you the first answer. The probability that Mei-Ling is chosen is, since every pair has equal probability to be chosen, equal to the fraction of pairs Mei-Ling is in. Another way to answer this question is to say that the probability Mei-Ling is chosen is equal to the probability any person is chosen. To find the answer to question 10 you can also count the number of pairs in which neither Sam nor Roberto are chosen and divide that by the total number of pairs.

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