Probability Word Problem

[Bens4vcobra]

A certain manufacturer of cake, muffin and bread mixes has 100 buyers, 50 of whom buy cake mix, 40 muffin mix and 20 buy both cake and muffin mix. If a buyer is to be selected at random from 100 buyers, what is the probability that the buyer will be one who purchases neither cake nor muffin mix?

A)1/10

B)3/10

C)1/2

D)7/10

E)9/10

I've seen this posted before but no good explanations as to WHY the answer is B were given.

[Frankenstein]

Hi,
n(cake) = 50
n(muffin) = 40
n(cake and muffin) = 20
So, n(Cake or muffin) = 50+40-20 = 70
So, the remaining 100-70 = 30 purchase neither of them
So, probability of picking such guy is 30/100 = 3/10.

Hence, B

[Brent@GMATPrepNow]

For these questions involving overlapping sets, I like to use the Double Matrix method. (see video at: https://www.beatthegmat.com/mba/2011/05/ ... question-1)

A lot of people use Venn diagrams, but I think Venn diagrams aren't as useful for keeping track of information when the question is complex.

Cheers,
Brent

[Bens4vcobra]

For these questions involving overlapping sets, I like to use the Double Matrix method. (see video at: https://www.beatthegmat.com/mba/2011/05/ ... question-1)

A lot of people use Venn diagrams, but I think Venn diagrams aren't as useful for keeping track of information when the question is complex.

Cheers,
Brent

I myself am a fan of the double set matrix for overlapping sets. Now that I see that this is, in fact, an overlapping set problem, it becomes quite easy. Thanks.

[edvhou812]

I used a venn diagram that had 20 as both muffin and cake, and then showed 30 as buying only cake, and 20 buying only muffins. This may sound confusing without a picture, but remember that 50 people bought cake, but included in that 50 are the 20 that bought both cake mix and muffin mix. So in the end we have: 20 both, 30 only cake, 20 only muffin for a total of 70 customers that bought muffin, cake, or both, which leaves 30 customer who didn't by either. Probability of randomly selecting a customer who buys neither is (100-70)/100 = 30/100 = 3/10.