Probability math

Question

There are 15 balls in a box, 6 of them are red, 5 are blue, 4 are yellow.

a) Find the probability of a randomly chosen ball is yellow one?

b) Chosen 2 balls, what is the probability that both balls are blue?

c) Chosen 3 balls, what is the probability that all these balls are of dierent color?

Answer 1

a) There are fifteen possible equally likely balls. Four of them are yellow. The probability of randomly choosing a yellow ball is 4/15.

b) There are C(15,2) possible pairs of balls from the box. There are C(5,2) possible pairs of blue balls. The probability of choosing 2 blue balls is c(5.2) / c(15,2) = (5*4 /2) / (15*14 / 2) = (5*4)/(15*14)

= 2/ 21

c) The are C(15,3) ways to choose a combination of 3 balls. In order to choose a combination of 3 balls with three different colors will imply choosing a red ball, a blue ball and a yellow ball. So there are 6*5*4 = 120 ways to do that. So the answer is 120 / c(15,3) = 120/455 = 24/91