Mr. Yutaro’s class contains 5 boys and 11 girls

There are several ways to solve this problem. One way is to calculate the chance that a boy is chosen first and then a girl is chosen second. This probability will be (5/16)(11/15) but this is only half the probability because we must also consider the chance that a girl is chosen first and then a boy. That probability is (11/16)(5/15). The odds are the same; only the numerators have changed places. Thus, we can simply calculate the probability as 2(11/16)(5/15).

This reduces to (11/8)(1/3) so the chances are 11/24, which is answer choice C.

lheiannie07 wrote:Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?

A. 9/48
B. 9/20
C. 11/24
D. 27/48
E. 13/16

P = (good outcomes)/(all possible outcomes).

All possible outcomes:
From 16 students, the number of ways to choose 2 = 16C2 = (16*15)/(2*1) = 120.

Good outcomes:
A good outcome consists of 1 boy and 1 girl.
Of the 16 students, 5 are boys, 16 are girls.
Thus:
Number of options for the boy = 5.
Number of options for the girl = 11.
To combine these options, we multiply:
5*11 = 55.

Resulting probability:
(good outcomes)/(all possible outcomes) = 55/120 = 11/24.

The correct answer is C.