Of the final five contestants in a television show, three are female and two are male. If two are chosen randomly to be the final contestants, what is the probability that both are female? Express your answer as a common fraction.

Guest Nov 2, 2019

#1**+1 **

The total possible outcomes = C(5,2) = 10

The number of outcomes that have two females is C(3,2) * C (2, 0) = 3 * 1 = 3

So....the probability =

3 / 10

CPhill Nov 2, 2019

#2**+1 **

*Of the final five contestants in a television show, three are female and two are male. If two are chosen randomly to be the final contestants, what is the probability that both are female? Express your answer as a common fraction.*

Out of the original five contestants, the odds that a female will be chosen are 3 out of 5 = 3/5

Out of the remaining four contestants, the odds that a female will be chosen are 2 out of 4 = 2/4

The odds of both the above happening are 3/5 times 2/4 = 6/20 = 3/10

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Guest Nov 2, 2019