A bag contains 4 blue and 5 green balls. Another bag contains 3 blue and 7 green balls. If one ball is drawn from each bag, what is the probability that two balls are of the same colour?

#### Solution

Let A be the event that a blue ball is drawn from each bag.

Probability of drawing one blue ball out of 4 blue balls where there are a total of 9 balls in the first bag and that of drawing one blue ball out of 3 blue balls where there are a total of 10 balls in the second bag is

P(A) = `4/9xx3/10`

Let B be the event that a green ball is drawn from each bag.

Probability of drawing one green ball out of 5 green balls where there are a total of 9 balls in the first bag and that of drawing one green ball out of 7 green balls where there are a total of 10 balls in the second bag is

P(B) = `5/9xx7/10`

Since both, the events are mutually exclusive and exhaustive events

∴ P(that both the balls are of the same colour)

= P(both are of blue colour) or P(both are of green colour)

= P(A) + P(B)

= `4/9xx3/10+5/9xx7/10`

= `12/90+35/90`

= `47/90`