Question

Mr. John needs some of his students to assist him in amathematics project for his class of 20 boys and 20 girls. Herandomly chooses one student who stands up. He thenchooses another student from those seated. What is theprobability that both students chosen are boys?

Answer 1

SOLUTION

The number of boys in the class is 20

And the total number of students in the class is 20+20=40

The probability of first picking a boy is:

$\frac{20}{40}$

Notice that after a boy has been picked then the number of boys will reduce by 1

Here the new number of boys is 19 and the number of students will become 39.

Therefore the probability of picking another boy is:

$\frac{19}{39}$

Therefore the probability of picking two boys is:

$\begin{gathered} \frac{20}{40}\times\frac{19}{39} \\ =\frac{1}{2}\times\frac{19}{39} \\ =\frac{19}{78} \end{gathered}$

Therefore the required probability is:

$\frac{19}{78}$