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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.

 Nov 2, 2019
 #1
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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

 

 

cool cool cool

 Nov 2, 2019
 #2
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+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

.

 Nov 2, 2019

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