Question

Twenty students compete in a school-wide marathon and each student is of comparable running ability. Of the 20 students, 15 were boys and 5 were girls. What is the probability that boys will place 1st, 2nd, and 3rd in the marathon?

Answer 1

Answer:

0.3991

Step-by-step explanation:

Number of Boys=15

Number of Girls =5

Total=15+5=20

Note that as each boy wins, the number of male contestants reduces. Thus is a probability of selecting an item without replacement.

P(1st boy winning) = 15/20

P(2nd boy winning) =14/19

P(3rd boy winning)=13/18

Therefore:

P(boys will place 1st, 2nd, and 3rd in the marathon)

= 15 /20 X 14/19 X 13/18

=91/228

=0.3991

Answer 2

Answer: The probability that boys will place first second and third in the race is 91/228

Step-by-step explanation:

Let's use another example to figure out how to tackle this particular question:-

If there e 12 black balls and 4 red balls in a box. If 3 balls are picked up at random without replacement, what is the probability that the 3 balls picked up at random are all black balls?

In this case, the total number of balls are: 12 + 4 = 16 balls.

Therefore the probability of picking up a red ball =

The number of red balls/ total number of balls in the box

= 4/16

Similarly, the probability of picking up a black ball =

12/16

So, if 3 balls are picked up at random without replacement, the probability that all will be black =

(12/16) × (11/15) × (10/14)

= 11/28

The probability that the 3 balls are all black balls is 11/28

If we then apply this principle to the question we were asked previously, we can determine the probability that boys will place first, second and third in the race.

Now, the total number of students partaking in the race =

15 boys + 5 girls = 20 students.

The probability of selecting a boy is :

Number of boys/total number of students

= 15/20

The probability of selecting 3 boys without replacement (which is the same thing as the probability that boys will place first, second and third in the race)

= (15/20) × (14/19) × (13/18)

= 91/228

The probability that boys will place first, second and third in the marathon is 91/228