Gian wrote:
A certain family consists of 8 adult members, including Susie.Each day, three stores A,B and C are operated by the family as follows:one of the 8 family members is selected randomly to operate store A,one of the remaining 7 family members is selected to operate store B, and finally one of the remaining 6 members is selected to operate store C. What is the probability that Susie will be selected to operate one of the three stores?
a) 1/3
b) 3/8
c) 1/24
d) 1/336
e) 1/512
We can look at this problem in terms of only 2 possible events: Either Susie will be selected to operate one of the stores, or she will not be selected to operate any stores. This means that:
P(Susie selected to operate one store) + P(Susie not selected to operate any stores) = 1
P(Susie selected to operate one store) = 1 - P(Susie not selected to operate any stores)
Thus, if we can determine the probability that Susie is not selected to operate any stores, then we’ll quickly be able to calculate the probability that she’ll be selected to operate one store.
We see that there are 8 family members, including Susie. Thus:
P(Susie does not get selected to operate store A) = 7/8
P(Susie does not get selected to operate store B) = 6/7
P(Susie does not get selected to operate store C) = 5/6
Total probability that Susie does not get selected to operate any store:
(7/8) x (6/7) x (5/6) = 6/8 x 5/6 = 5/8
Thus, the probability that Susie is selected to operate one of the stores is 1 - 5/8 = 3/8.
Alternative solution:
The probability that Susie will be selected to operate one of the three stores is the probability that she will operate store A or store B or store C. That is:
P(Susie will operate any one of the three stores) = P(she will operate store A) + P(she will operate store B) + P(she will operate store C)
Let’s find the probability that she will operate any one of these 3 stores (keep in mind that if she works at one store, she can’t work at the other two):
P(she will operate store A) = P(A, not B, not C) = 1/8 x 7/7 x 6/6 = 1/8
P(she will operate store B) = P(not A, B, not C) = 7/8 x 1/7 x 6/6 = 1/8
P(she will operate store C) = P(not A, not B, C) = 7/8 x 6/7 x 1/6 = 1/8
Therefore:
P(Susie will operate any one of the three stores) = 1/8 +1/8 + 1/8 = 3/8
Answer: B