Answer:
[tex]\dfrac{90}{341}[/tex]
Step-by-step 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:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Probability of picking a boy from 3rd grade, [tex]P_{1} = \dfrac{15}{31} ..... (1)[/tex]
Probability of picking a boy from 4th grade, [tex]P_{2} = \dfrac{18}{33} ..... (2)[/tex]
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.
[tex]P = P_{1} \times P_{2}\\\Rightarrow \dfrac{15}{31} \times \dfrac{18}{33}\\\Rightarrow \dfrac{90}{341}[/tex]
