Probability problem

[tacobell]

A manufacture of A, B, and C has 100 buyers of whom 50 purchase A, 40 purchase B, and 20 purchase both A and B. If a buyer is selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchase nether A or B?

1/10
3/10
1/2
7/10
9/10

Thanks in advance.

[Stuart@KaplanGMAT]

A manufacture of A, B, and C has 100 buyers of whom 50 purchase A, 40 purchase B, and 20 purchase both A and B. If a buyer is selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchase nether A or B?

1/10
3/10
1/2
7/10
9/10

Thanks in advance.

Great case for the overlapping sets formula:

True # of items = # with charactersitic 1 + # with characteristic 2 + # with neither 1 nor 2 - # with both characteristics

In this case:

100 = 50 + 40 + neither - 20

100 = 70 + neither

30 = neither

The question asks for the probability that a random buyer falls into the "neither" category.

Prob = #desired/total# = 30/100 = 3/10: choose (b).

[ajguerre]

This problem is easy if you use VENN diagrams but since I cannot post that I'll try to reflect it using an equation:

Total # of Buyers = A + B - BOTH + NEITHER = 50 + 40 -20 + x

100 = 70 + x

x = 30

Then the probability will be 30 / 100 = 3 / 10