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?

Question

asked Jul 13, 2022 19.5k views

1 Answer

AlvaroSantisteban · Answer 1 · 2022-07-19T03:14:15+0000

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
.