Question

A bag contains 6 red balls and 9 black balls. Two balls are drawn, one after the other with replacement. Find the probability that

a. Both are of the same colours
b. Both are of different colours

Answer 1

a) 13/25

b) 12/15

Explanation:

a) Since it is with replacement, the chance of them being both the same colour will be

P(both red) + P(both black) = (6/15*6/15) + (9/15*9/15)

= 13/25

b) If they are both different colours, then we will be working out

P(both colours) = (6/15*9/15)*2 = 12/25 (Its *2 because the other way of pulling both colours is 9/15*6/15 which is the same but flipped)

Another way of working this question out is

P(1-All red or all blue) which from above we know that All red or all blue is 13/25 so

P(1-All red or all blue) = 1 - 13/25 = 12/25