A bag contains 6 balls. If 4 balls are drawn at a time and all of them are found to be red, then the probability that exactly 5 of the balls in the bag are red is

Step-by-step solution

Let us define the following events E= drawn balls are red. A=4 red balls in bag. B=5 red balls in bag. C=6 red balls in bag. Then, P(A)=P(B)=P(C) and aligned P ( E A ) & = ^4 C₄ ^6 C₄ = 1 15 P ( E B ) & = ^5 C₄ ^6 C₄ = 5 15 and P ( E C )= ^6 C₄ ^6 C₄ = 15 15 aligned By applying Baye's theorem, gathered P ( B A )= P(B) P ( E B ) P(A) P ( E A )+P(B) P ( E B )+P(C) P ( E C ) = 5 15 1 15 + 5 15 + 15 15 = 5 21 gathered