Ms. Katz's second grade class is composed of an equal number of boys and girls. If Ms. Katz chooses 3 students at random to work on a project, what is the probability that at least 2 of them will be girls?
(1) There are 18 students in Ms. Katz's class.
(2) The probability that all 3 students chosen are girls is 7/68
Statement 1: There are 18 students in Ms. Katz's class.
Since the class is composed of an equal number of boys and girls, there are 9 boys and 9 girls.
Since we know the total number of boys and the total number of girls, we can determine the probability that at least 2 of the 3 students chosen will be girls.
SUFFICIENT.
Statement 2: The probability that all 3 students chosen are girls is 7/68.
Check whether the values in statement 1 also satisfy statement 2.
If there are 18 students in total -- in other words, 9 boys and 9 girls -- then P(GGG) = 9/18 * 8/17 * 7/16 = 7/68.
If the total number of students is equal to ANY OTHER VALUE -- if there are 2 boys and 2 girls, or 10 boys and 10 girls -- then the constraint that P(GGG) = 7/68 will NOT be satisfied.
Thus, the ONLY values that satisfy statement 2 are those implied by statement 1: total boys = 9, total girls = 9.
SUFFICIENT.
The correct answer is
D.
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