probability

Expert replies

hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 amFollowed by: 2 members; Thanked: 9 times

by hey_thr67 » Tue Jun 26, 2012 10:53 am

If Ben were to lose the championship, Mike would be the winner with a probability of 1/4, and Rob 1/3. If the probability of Ben being the winner is 1/7, what is the probability that either Mike or Rob will win the championship?

A: 1/12
B: 1/7
C: 1/2
D: 7/12
E: 6/7

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jun 26, 2012 10:53 am

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

by eagleeye » Tue Jun 26, 2012 2:14 pm

This is a combined probability problem.

Let Probability of Ben, Mike and Rob winning be P(B), P(M), P(R) respectively.

Then we are told that, when Ben doesn't win, the probability of Mike winning is 1/4 and that of Rob is 1/3. Now probability of Ben losing = P(#B) = 1-P(B). (where I have used #B to show the event of Ben not winning. Remember that probability of one winning and the other two also winning is 0.
The event that Ben loses and Mike wins is denoted by (#BM). Now P(#BM) = P(#B)*P(M).

So, we are given that
P(#B)*P(M) = 1/4
P(#B)*P(R) = 1/3
Then we are told that P(B) = 1/7. So P(#B) = 1-1/7 = 6/7.

We need to find probability of either Mike or Rob winning. So we need P(M)+P(R).

In the first two equations, substituting P(#B) = 6/7 and adding them, we get
6/7*(P(M)+P(R)) = 1/4 + 1/3 => P(M)+ P(R) = (1/3+1/4)*6/7 = 7/12*6/7 = 1/2.

Hence C is the right answer.

Let me know if this helps

Like this post

GMAT/MBA Expert

Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

by Mike@Magoosh » Tue Jun 26, 2012 2:21 pm

hey_thr67 wrote:If Ben were to lose the championship, Mike would be the winner with a probability of 1/4, and Rob 1/3. If the probability of Ben being the winner is 1/7, what is the probability that either Mike or Rob will win the championship?

A: 1/12
B: 1/7
C: 1/2
D: 7/12
E: 6/7

Hi, there. I'm happy to help with this.

This is a tricky question. First of all, P(Ben wins) = 1/7, so P(Ben doesn't win) = 1 - 1/7 = 6/7.

The wording of the first part is very important: If Ben were to lose the championship, Mike would be the winner with a probability of 1/4, and Rob 1/3. This is a conditional probability --- we are told the probability given that a certain condition (Ben losing) is met.

The conditional probability of A, given B, is written P(A|B). The formula for this is

P(A and B) = P(B)*P(A|B)

Here, B = Ben loses, and we want A = Mike or Rob wins.

P(Mike wins|Ben loses) = 1/4
P(Rob wins|Ben loses) = 1/3

Add these two:
P(Mike wins|Ben loses) + P(Rob wins|Ben loses) = P(Mike or Rob wins|Ben loses) = 1/4 + 1/3 = 7/12

P(Mike or Rob wins) = P(Ben loses)*P(Mike or Rob wins|Ben loses) = 6/7 * 7/12 = 6/12 = 1/2

Answer = C

Again, that was a very hard question. This is at the very outer limit of what the GMAT could possible ask. Here's a much more typical kind of GMAT math probability question.

https://gmat.magoosh.com/questions/1036
When you submit your answer to this question, the next page will have the full video solution.

Let me know if you have any more questions.

Mike

Magoosh GMAT Instructor
https://gmat.magoosh.com/

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 26, 2012 3:21 pm

hey_thr67 wrote:If Ben were to lose the championship, Mike would be the winner with a probability of 1/4, and Rob 1/3. If the probability of Ben being the winner is 1/7, what is the probability that either Mike or Rob will win the championship?

A: 1/12
B: 1/7
C: 1/2
D: 7/12
E: 6/7

When we want one event AND another event to happen -- P(A AND B) -- we MULTIPLY the fractions.
When we want one event OR another event to happen -- P(A OR B) -- we ADD the fractions.

Since P(Ben wins) = 1/7, P(Ben loses) = 6/7.

Case 1: Ben loses AND Mike wins.
Since we want both events to happen, we multiply:
6/7 * 1/4 = 3/14.

Case 2: Ben loses AND Rob wins.
Since we want both events to happen, we multiply:
6/7 * 1/3 = 2/7.

Since either Case 1 OR Case 2 will yield a good outcome, we add the results above:
3/14 + 2/7 = 3/14 + 4/14 = 7/14 = 1/2.

The correct answer is C.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review