The probability that the teacher will choose a boy at random the first time is 7/10. After the first boy is picked, that leaves 9 people remaining, 3 girls and 6 boys, giving us a chance that a boy will be picked 6/9, or 2/3 of the time. We can multiply these fractions to give us the final chance two boys will be picked. 7/10 x 2/3 = 7/15 in simplest form. The teacher will choose two boys 7/15 of the time.