Question

An ordinary dice is tossed once. If a 1 appears, a ball is drawn from Urn 1. If a 2, 3 or 4 appears, a ball is drawn from Urn 2; otherwise, a ball is drawn from Urn 3. Urn 1 contains 5 white, 3 green and 2 red balls. Urn 2 contains 1 white, 6 green and 3 red balls. Urn 3 contains 3 white, 1 green and 6 red balls. What is the probability that a red ball is drawn?

Answer 1

Required probability $= (\frac{1}{6})(\frac{2}{10})+(\frac{3}{6})(\frac{3}{10})+(\frac{2}{6})(\frac{6}{10})$

So required probability $= P(red \; ball) =\frac{23}{60} = 0.3833$