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

a) 13/25

b) 12/15

Step-by-step 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