Question

A bag contains 10 red marbles, 5 white marbles, and 5 blue marbles. You draw 5 marbles out at random, without replacement.

What is the probability that all the marbles are red?

What is the probability that exactly two of the marbles are red?

What is the probability that none of the marbles are red?

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

P(all the marbles are red) = Number of ways to select 5 red marbles from 10 / Number of ways to select 5 marbles from total 20

= 10C5 / 20C5

= 252/15,504

= 0.0163

P(exactly two of the marbles are red) = Number of ways to select 2 red marbles from 10 x Number of ways to select 3 other marbles from remaining 15 / Number of ways to select 5 marbles from total 20

= 10C2 x 10C3 / 20C5

= 45 x 120 / 15,504

= 0.3483

P(none of the marbles are red) = Number of ways to select 5 non-red marbles from 10 / Number of ways to select 5 marbles from total 20

= 10C5 / 20C5

= 252/15,504

= 0.0163