trangle wrote:A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 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 the one who purchases neither cake mix nor muffin mix?

a. 1/10
b. 3/10
c. 1/2
d. 7/10
e. 9/10

Total = Cake mix + Muffin mix - Both + Neither
=> 100 = 50 + 40 - 20 + Neither
=> Neither = 30

Hence, required probability = 30/100 = 3/10

The correct answer is B.

trangle wrote:what about bread mix?

The question is neither asking anything about the bread mix nor it has provided any information about bread mix. If you are still not sure, you can try the following approach, but I must warn you it's more complicated than necessary.

Total = Cake + Muffin + Bread - Cake & Muffin - Cake & Bread - Muffin & Bread + Cake, Muffin & Bread

Now the question asks about neither Cake nor Muffin.
Neither Cake nor Muffin = Only Bread = (Bread - Cake & Bread - Muffin & Bread + Cake, Muffin & Bread)

Now replace this term in bracket with "Neither Cake nor Muffin" in the first equation.
=> Total = Cake + Muffin - Cake & Muffin + Neither Cake nor Muffin
=> 100 = 50 + 40 - 20 + Neither Cake nor Muffin
=> Neither Cake nor Muffin = 30

Hope it is clear now.