A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

Step-by-step solution

Let the bag contains black balls B and non-black balls B ¯ , then we can have the following possibilities: 6 B , 0 B ¯ ,   5 B , 1 B ¯ ,   4 B , 2 B ¯ ,   3 B , 3 B ¯ , 2 B , 4 B ¯ All the events are equally likely, i.e., 1 5 . Required probability = 1 5 × C 2 6 C 2 6 + 1 5 × C 2 5 C 2 6 1 5 × C 2 6 C 2 6 + 1 5 × C 2 5 C 2 6 + 1 5 × C 2 4 C 2 6 + 1 5 × C 2 3 C 2 6 + 1 5 × C 2 2 C 2 6 = 25 35 = 5 7