Question

A bag contains 6 red balls, 11 yellow balls and 5 pink balls. If two balls are drawn at random from the bag, one after another, what is the probability that the first ball drawn was red and the second ball drawn was yellow in colour?

Accepted Answer

C. Total number of balls = $6 + 11 + 5 = 22$. Probability of drawing a red ball first: $$P(	ext{Red}_1) = \frac{6}{22}$$ After drawing one red ball, 21 balls remain in the bag. Probability of drawing a yellow ball second: $$P(	ext{Yellow}_2 | 	ext{Red}_1) = \frac{11}{21}$$ Combined probability: $$P = \frac{6}{22} 	imes \frac{11}{21} = \frac{3}{11} 	imes \frac{11}{21} = \frac{3}{21} = \frac{1}{7}$$

Probability of Red and Yellow Balls

Explanation

Practise this under exam conditions