Question

A third grade class has 16 girls and 15 boys a fourth grade class has 18 boys and 15 girls when picking for PE captains will make one selection from the fourth grade class and one selection from the third grade class before the other team pics assuming everyone has an equally like lee chance of being selected what is the probability that the first captain will choose two boys on the first pick

Answer 1

a

Explanation:

Answer 2

`(90)/(341)`

Explanation:

3rd grade:

Number of girls = 16

Number of boys = 15

Total number of students = 31

4th grade:

Number of girls = 15

Number of boys = 18

Total number of students = 33

Formula for probability of an event E can be observed as:

`P(E) = \frac{\text{Number of favorable cases}}{\text {Total number of cases}}`

Probability of picking a boy from 3rd grade,
`P_(1) = (15)/(31) ..... (1)`

Probability of picking a boy from 4th grade,
`P_(2) = (18)/(33) ..... (2)`

These are two independent events of picking a boy from 3rd grade and 4th grade.

So, probability the captain chooses 2 boys in the first pick can be found by multiplying (1) and (2) above.

`P = P_(1) * P_(2)\\\Rightarrow (15)/(31) * (18)/(33)\\\Rightarrow (90)/(341)`