A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Two marbles are drawn from the bag. Which expression represents the probability that one of the marbles is red and the other is blue?
Answer
A
the fraction with numerator sub 30 cap p sub 2 and denominator sub 50 cap p sub 2
B
the fraction with numerator open paren sub 10 cap p sub 1 close paren times open paren sub 20 cap p sub 1 close paren and denominator sub 50 cap p sub 2
C
the fraction with numerator sub 30 cap c sub 2 and denominator sub 50 cap c sub 2
D
the fraction with numerator open paren sub 10 cap c sub 1 close paren times open paren sub 20 cap c sub 1 close paren and denominator sub 50 cap c sub 2
Explanation
There are 50 marbles total, so the number of ways to draw any 2 marbles is 50 C 2. For a favorable draw, choose 1 of the 10 red marbles and 1 of the 20 blue marbles, giving (10 C 1)(20 C 1) ways. Thus the probability is the fraction with numerator (10 C 1) times (20 C 1) and denominator 50 C 2, which is choice D.
AI-written and checked against the verified answer.