a If nB 16 nA B 21 and nA B 3 find nA b If nA 24 nB 2

a) If n(B) = 16, n(A ? B) = 21, and n(A ? B) = 3, find n(A).

b) If n(A) = 24, n(B) = 20, n(C) = 20, n(A ? B) = 5, n(A ? C) = 7, n(B ? C) = 4, and n(A ? B ? C) = 50, find n(A ? B ? C).
c) Of 200 clock radios with digital tuners and/or CD players sold recently in a department store, 140 had digital tuners and 180 had CD players. How many radios had both digital tuners and CD players?

d) A female executive selecting her wardrobe purchased two blazers, five blouses, and four skirts in coordinating colors. How many ensembles consisting of a blazer, a blouse, and a skirt can she create from this collection?

Solution

a. n(A) = n(A or B) + n(A and B) - n(B) = 21 + 3 - 16 = 8

b. P( A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)

50 = 24 + 20 + 20 - 5 - 7 - 4 + P(A and B and C)

P(A and B and C) = 2

c. P(radio and digital) = 140 + 180 - 200 = 120

d. Number of ways = 2C1 * 5C1 * 4C1 = 40