probability (cake, muffin, and bread mixes)

[LevelOne]

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 one who purchases neither cake mix nor muffin mix?

A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10

thanks

[rahulg83]

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 one who purchases neither cake mix nor muffin mix?

A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10

thanks

Total no of purchasers = 100 , say T
remember, don't worry about bread mix purchasers as no info is given on them...
cake purchasers = C = 50
muffin purchasers = M =40, Both (C and M) = 20

Total no = cake + muffin - both (cake and muffin) + rest of them (may be bread, we are not concerned)

100 = 50+40-20+other
other= 30

Now probability that a buyer selected at random will be one who purchased neither muffin mix or cake mix = 30C1/100C1 = 3/10 Ans..

[LevelOne]

OA is B, the same as your answer.