Question

A bag contains 10 balls: 4 white and 6 black.

A ball is removed at random and replaced; a second ball is then removed.
What is the probability that the balls removed were the same colour?
(Answer is in its simplest form.)

Answer 1

first case

1. probability of white ball in first replacement P(w)=4/10
2. probability of black ball in first replacement P(b)=6/10
3. probability of white ball in second replacement P'(w)=3/9
4. probability of black ball in second replacement P'(b)=5/9

Explanation:

now for ,

the probability that the balls removed were the same colour =P(w)×P'(w)+P'(b)×P(b)

=7/15