Question

A school basketball club consists of 5 girls and 11 boys. For the next game 5 persons are randomly chosen to take the following positions: point guard, shooting guard, small forward, power forward and center. Specify a probability space for the experiment and calculate the probabilities of the following events: A: All players are girls; B: All players are boys; C: Small forward is the only girl; D: Small forward and point guard are girls.

Answer 1

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Given that:

Girls 5

Boys 11

5 people are randomly selected for positions .

a. P(all players are girls) = choose 5 from 5 girls/ choose any 5 from any 16 total students = 5C5 / 16C5 = 1/4368

b. P(all players are boys) = choose 5 from 11 boys / choose any 5 from 16 total students = 11C5 / 16C5 = 462/4368 = 0.1058

c. P(small forward is the only girl) = choose 1 from 5 girls, the rest 4 positions from 11 boys/ choose any 5 from 16 students

= 5C1*11C4 / 16C5 = 5*330/4368 = 0.3778

d. P(small forward and point guard are girls) = Choose 2 from 5 girls, rest 3 from 11 boys / choose any 5 from 16 students

= 5C2*11C3 / 16C5 = .3778