Question

A bag has 5 green and 6 yellow tennis balls. If two are picked at random, find the probability that at least one of them is green in color. please explain how to get the answer for future reference.

Answer 1

8/11.

Explanation:

There are a total of 11 balls.

At least one of those picked is green means that 1 or 2 green balls are picked in the two trials.

Prob (First one picked is green) = 5/11.

Prob( second one picked is green) = 4/10 = 2/5.

Therefore Prob ( Green then green) = 5/11 * 2/5 = 10/55 = 2/11.

The other possibilities are Green then Yellow OR Yellow then Green.

The probabilities of these are worked out as above and come to

5/11 * 6/10 and 6/11 * 5/10

= 300/110 and 30/110

= 3/11 and 3/11.

Finally the Prob ( 2G OR G&Y OR Y&G) = 2/11 + 3/11 + 3/11

= 8/11.

I just realised there is an easier way to do this. Much less work.

The only other thing that can happen other than ' at least one green' is '2 yellows' so the required probability is

1 - prob(2 yellows)

= 1 - (6/11 * 5/10)

= 1 - 30 /110)

= 1 - 3/11

= 8/11.

But never mind. I hope the above is instructive and helps you understand.