Probability Word Problem

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Bens4vcobra: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members; Thanked: 3 times

by Bens4vcobra » Tue Jul 05, 2011 6:18 am

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.

"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban

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Source: Beat The GMAT — Problem Solving | Tue Jul 05, 2011 6:18 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Jul 05, 2011 6:35 am

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

Cheers!

Things are not what they appear to be... nor are they otherwise

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Jul 05, 2011 8:38 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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Bens4vcobra: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members; Thanked: 3 times

by Bens4vcobra » Tue Jul 05, 2011 9:05 am

Brent@GMATPrepNow wrote: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.

"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban

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edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Tue Jul 05, 2011 11:32 pm

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.

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