Question

Suppose that an opaque jar contains 10 red tea bags and 11 blue tea bags. Assume that these tea bags are indistinguishable from each other except their labels.

Answer the following questions. If necessary, round your answers to four decimal places.

(a) How many ways can you randomly pick out 5 tea bags from the jar?

(b) What is the probability that you randomly pick out 5 tea bags and exactly 4 of them are red tea bags?

(c) What is the probability that you pick up a red tea bag first (without putting it back into the jar), then pick up a blue tea bag second?

Answer 1

(a)

Total there are 10+11=21 tea bags.

The number of ways of selecting 5 tea bags from a group of 21 tea bags is given by

Note that here the order of selection is not important as tea bags are indistinguishable from each other except their labels and hence we have combination.

(b) We want to find the probability that you randomly pick out 5 tea bags and exactly 4 of them are red tea bags.

Total number of red tea bags is 10.

Number of ways of selecting 4 red tea bags is

The remaining 1 tea bag should be blue and there are 11 blue tea bags and one blue can be any of these

Hence probability that you randomly pick out 5 tea bags and exactly 4 of them are red tea bags

(c)

We want to find the probability that you pick up a red tea bag first (without putting it back into the jar), then pick up a blue tea bag second .

There are total 21 tea bags and out of these are 10 red bags.

So probability of selecting a red tea bag first is

Once you select a red tea bag as we are not putting it back into the jar, we are left with 20 tea bags out of which 9 are red and 11 are blue.

So probability of selecting a blue tea bag from this group of tea bags is

Hence