Answer to Question #10437 in Statistics and Probability for John Waters

Question

A bag contains five green marbles and three red marbles. If three marbles are chosen at random without replacement, what is the probability that all three will be green?

Answer 1

There are C(5,3) ways to choose three green marbles from five green marbles, and all these results are successful. The total number of possible ways to choose three marbles from five green marbles and three red marbles is C(5+3,3). So,

P = C(5,3)/C(5+3,3) = C(5,3)/C(8,3) = 10/56 ≈ 0.1786.