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There are 10 girls and 15 boys in a race. What is the probability that the first, second and third place winners will be boys?

User Bladekp
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1 Answer

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Given:

Number of girls = 10

Number of boys = 15

To find:

The probability that the first, second and third place winners will be boys.

Solution:

Total number of boys and girls:


10+15=25

The probability that the first place winner will be a boy is


P(\text{Boy at first place})=(15)/(25)

Now, the remaining number of boys is 14. So, the probability that the first place winner will be a boy is


P(\text{Boy at second place})=(14)/(24)

Now, the remaining number of boys is 13. So, the probability that the first place winner will be a boy is


P(\text{Boy at third place})=(13)/(23)

The probability that the first, second and third place winners will be boys is


P(BBB)=(15)/(25)* (14)/(24)* (13)/(23)


P(BBB)=(3)/(5)* (7)/(12)* (13)/(23)


P(BBB)=(1)/(5)* (7)/(4)* (13)/(23)


P(BBB)=(91)/(460)

Therefore, the probability that the first, second and third place winners will be boys is
(91)/(460).

User AlvaroSantisteban
by
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