1
lesson pretestMultiple Choice

Pretest

Question 1 • Mathematics II

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the probability that both students chosen are sophomores?

Answer
A
the fraction with numerator sub 6 cap p sub 2 and denominator sub 20 cap p sub 2
B
the fraction with numerator open paren sub 20 cap p sub 6 close paren times open paren sub 19 cap p sub 5 close paren and denominator sub 20 cap p sub 2
C
the fraction with numerator 6 cap c sub 2 and denominator 20 cap c sub 2
D
the fraction with numerator open paren sub 20 cap c sub 6 close paren times open paren sub 19 cap c sub 5 close paren and denominator sub 20 cap c sub 2

Explanation

There are 20 students total, and two positions are being filled without regard to order. The number of ways to choose any two students is 20C2, while the number of ways to choose two sophomores from the six is 6C2. Therefore, the probability is (6C2)/(20C2), which is choice C.

AI-written and checked against the verified answer.

Next