Question

A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag and 2 balls are drawn from the second bag, then find the probability that all three balls are of the same colour.

Answer 1

Possible selections are as follows:

1 red ball from bag-I, 2 red balls from bag-II

or 1 white ball from bag-I, 2 white balls from bag-II

∴ Probability of drawing three balls of the same colour

i.e., P(E) = `(""^3"C"_1)/(""^7"C"_1) xx (""^2"C"_2)/(""^5"C"_2) + (""^4"C"_1)/(""^7"C"_1) xx (""^3"C"_2)/(""^5"C"_2)`

= `3/7 xx 1/10 + 4/7 xx 3/10`

= `3/70 + 12/70`

= `15/70`

∴ P(E) = `3/14`