Question

A bag contain 8 red and 5 white balls. Three balls are drawn at random. Find the probability that: All the three balls are white. All the three balls are red. One ball is red and two balls are white. Select the correct answer from above options

Answer 1

∴Number of red balls =8 and number of white balls 5 (i) P(all the three balls are white) = .5C3 .13C3 = 5! 3!2! 13! 3!10! = 5! 3!2! × 3!10! 13! = 5×4×3×2! 2! × 10! 13×12×11×10! = 5×4×3 13×12×11 = 5 13×11 = 5 143 5×4×3 13×12×11 = 5 13×11 = 5 143 (ii) P(all the three balls are red) = .8C3 .13C3 = 8! 315! 13! 3!10! = 8! 3!×5! × 3!10! 13! = 8×7×6×5! 5! × 10! 13×12×11×10! = 8×7×6 13×12×11 = 28 143 (iii) P(one ball is red and two balls are white)= .8C1 .13C3 = 8×10 13×6×11 = 40 143