A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 17 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Choose the correct choice from the following options.
A) 1/10	B) 3/10	C) 1/2	D) 27/100	E) 9/100
C+M+B-CM-MB-CB-2CMB = 100   C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-17-2CMB = 100   B-CB-MB-2CMB = 27   hence the probability = 27/100   27/100
<result>D</result>
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 17 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?