From a small town 120 people were randomly selected and aske

From a small town, 120 people were randomly selected and asked the following question: Which of these three stores do you visit weekly (at least once per week), Store A, Store B, or Store C? The following results were obtained: 20 visit Store A and Store C, 10 visit Store A and Store B but not Store C, 15 visit ail three stores. 30 only visit Store C, 35 visit Store B but not Store C. 25 visit Stores B and C, and 10 visit neither of the three stores. If a person Ls randomly selected from this group of 120, what is the probability that he or she will visit Store B and Store C? visits at least one of the three stores in the next week? does not visit Store A or does not visit Store C? only visits Store B? only visits Store A?

Solution

From the given data let them represent in set theory.

Let A = visitors for store A, B for B and C for store C

n(AC) = 20: n(ABC\') = 10

n(ABC) = 15

n(C) = 30

n(BC\') = 35

n(BC) = 25

n(A\'B\'C\') = 10

Let us draw Venn diagram for this.

Note: 10 outside are those who visit none.

A alone 45 is the balancing figure.

B - C = 35 Hence 25 for B alone we got.

a) B and C visitors = 10+15+10 = 35

b) n(AUBUC) = 120-10 = 110

c) n(A\'UC\') = n(AC)\' = 120-20 =100

d) Only visits store B = 25

e) Only visits store A =45