1. A group of 6 volleyball players, Ally, Brad, Claire, Devon, Ewing, and Frank
ID: 2930483 • Letter: 1
Question
1. A group of 6 volleyball players, Ally, Brad, Claire, Devon, Ewing, and Frank are going to play doubles (two on each team). Suppose that they decide to draw four names out of a hat in order to see which four of them will play first, and answer the following questions: a. List out the sample space for the possibilities for the first group to play. (5 pts) b. Based on the sample space, what is the probability that Ally will play in the first group? (3 pts) c. What is the probability of at least 1 female in the first group (Ally and Claire are female)? (3 pts) What is the probability of only 1 female or only 3 males in the first group? (5 pts)
Explanation / Answer
a) The sample space for the possible four players who would play the first game would be given as:
S = { ABCD, ABCE, ABDE, ACDE, BCDE, ABCF, ABDF, ABEF, ACDF, ACEF, ADEF, BCDF, CDEF, BDEF, BCEF }
There are 15 elements int he sample space here.
b) The probability that Ally will play in the first group can be computed as the number of outcomes in the above sample space where A is there divided by the total number of elements in the sample space
= 10/15
= 2/3
= 0.6667
Therefore 0.6667 is the required probability here.
c) Here we are given that A and C are females. Now probability that at least 1 female play would be computed as:
= 1 - Probability that no female plays
= 1 - Probability that BDEF plays
= 1 - (1/15)
= 14/15
= 0.9333
Therefore 0.9333 is the required probability here.
d) Probability that only 1 female or only 3 males play is computed as:
= Number of ways to choose 1 female from 4 females * Number of ways to choose 3 males from 4 males / Total number of combinations
= 2*4 / 15
= 8/15
= 0.5333
Therefore 0.5333 is the required probability here.
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