Question

A bin contains 4 red and 6 blue balls and three balls are drawn at random. Find the probability such that both are of the same color.

(a) \(\frac{10}{28}\)

(b) \(\frac{1}{5}\)

(c) \(\frac{1}{10}\)

(d) \(\frac{4}{7}\)

The question was posed to me by my college professor while I was bunking the class.

I'd like to ask this question from Discrete Probability topic in portion Discrete Probability of Discrete Mathematics

Answer 1

Right option is (b) \(\frac{1}{5}\)

Best explanation: Total no of balls = 10. Number of ways drawing 3 balls at random out of 10 = ^10C3 = 120. Probability of drawing 3 balls of same colour = ^4C3 + ^6C3 = 24. Hence, the required probability is \(\frac{24}{120} = \frac{1}{5}\).