A druggist wishes to select three brands of aspirin to sell

A druggist wishes to select three brands of aspirin to sell in his store. He has five major brands to choose from: A, B, C, D and E. If he selects the three brands at random, what is the probability that he will select the following?

(a) brand B


(b) brands B and C


(c) at least one of the two brands B and C

Solution

a)

There are 5C3 = 10 ways to choose any 3 brands.

If one is already B, then there are 4C2 = 6 ways to choose the other two.

Thus,

P(B) = 6/10 = 0.6 [answer]

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b)

If there\'s already B and C, there are only 3 ways to choose the last one. Thus,

P(B and C) = 3/10 = 0.3 [answer]

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c)

Here,

P(B) = P(C) = 0.6

P(B and C) = 0.3

As

P(B or C) = P(B) + P(C) - P(B or C)

Then

P(B or C) = 0.6 + 0.6 - 0.3 = 0.9 [ANSWER]