Question

Problem #2

A salesperson with three products A, B, and C called 200 customers over a period of time.  These 200 customers placed orders as follows:

100 ordered product A           55 ordered products A and C

95 ordered product B             30 ordered products B and C

85 ordered product C             20 ordered products A and B and C

50 ordered products A and B

Determine the number of customers who ordered

1. at least one product,
2. no products
3. exactly one product,
4. exactly two products,
5. exactly three products

Show your work

Answer 1

n(A and C only ) = n(A and C) - n (all 3) = 55 - 20 = 35
n(B and C only ) = n(B and C) - n(all 3) = 30 - 20 = 10
n(A and B only ) = n(A and B) - n(all 3) = 50 - 20 = 30

n(A only ) = n(A) - n(A and C only ) - n(A and B only ) - n(all 3) = 100 - 35 - 30 - 20 = 15
n(B only ) = 95 - 10 - 30 - 20 = 35
n(C only ) = 85 - 35 - 10 - 20 = 20

a) n(at least one ) = 35 + 10 + 30 + 15 + 35 + 20 + 20 = 165
b) n(no products) = 200 - n( at least one ) = 200 - 165 = 35
c) n(exactly one product ) = 15 + 35 + 20 = 70
d) n(exactly two products) = 35 + 10 + 30 = 75
e) n(all three products ) = 20