A box contains identical balls of which 12 are red, 16 white and 8 blue. Three balls are drawn from the box one after the other without replacement. Find the probability that : (a) three are red; (b) the first is blue and the other two are red; (c) two are white and one is blue.
Explanation
n(R) = number of red balls = 12; n(W) = number of white balls = 16; n(B) = number of blue balls = 8 Total number of balls = 36 (a) P(three are red) = \(\frac{12}{36} \times \frac{11}{35} \times \frac{10}{34}\) = \(\frac{11}{357}\) (b) P(first is blue and other two red) = \(\frac{8}{36} \times \frac{12}{35} \times \frac{11}{34}\) = \(\frac{44}{1785}\) (c) P(two are white and one is blue) = \(\frac{16}{36} \times \frac{15}{35} \times \frac{8}{34}\) = \(\frac{16}{357}\)