Contidional Probability?

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sumithshah: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed May 28, 2008 11:25 pm; Thanked: 9 times; GMAT Score:730

by sumithshah » Sat Sep 27, 2008 11:13 pm

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 , what is the probability that either Mike or Rob will win the championship?

1/12 ; 1/7 ; 1/2 ; 7/12 ; 6/7

OA C

I have no clue how do this. Any pointers would be appreciated

Last edited by sumithshah on Sun Sep 28, 2008 12:24 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sat Sep 27, 2008 11:13 pm

manulath: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Tue Sep 09, 2008 10:12 pm; Location: Lko; Thanked: 3 times

by manulath » Sat Sep 27, 2008 11:58 pm

please check the question, it is missing data - prababilities!
regards

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sumithshah: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed May 28, 2008 11:25 pm; Thanked: 9 times; GMAT Score:730

by sumithshah » Sun Sep 28, 2008 12:24 am

fixed

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Sun Sep 28, 2008 2:37 am

not fixed yet

winner is ???????, what is the

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manulath: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Tue Sep 09, 2008 10:12 pm; Location: Lko; Thanked: 3 times

Re: Contidional Probability?

by manulath » Sun Sep 28, 2008 3:17 am

[quote="sumithshah"]If the probability of Ben being the winner is ,

Please correct the question. Data missing.

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

Re: Contidional Probability?

by sudhir3127 » Sun Sep 28, 2008 3:27 am

sumithshah 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 , what is the probability that either Mike or Rob will win the championship?

1/12 ; 1/7 ; 1/2 ; 7/12 ; 6/7

OA C

I have no clue how do this. Any pointers would be appreciated

This is the right Question

"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?" Sumit would appreciate if u double check before posting a Question .. it would unnecessarily delay the posters time ....

here goes the Answer...

Prob of Ben wins=1/7

Prob of ben loses =6/7.

P(Mike wins or Rob wins) = P(Mike wins)+P(Rob wins) - P(Both wins)
=1/4+1/3-0
=7/12.

But we are only 6/7 sure about Ben loosing.

hence the probability is = 6/7*7/12=1/2

hope that helps....

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Fri Sep 18, 2009 5:30 pm

P(Mike winning)=P(Ben looses). P(Mike wins) . P(Rob looses)
P(Rob winning)=P(Ben looses). P(Mike looses) . P(Rob wins)

Adding the two will give us the answer right?

Now given,P(mike wins)=1/4.Therefore,P(mike looses)=3/4
Similarly,P(rob wins)=1/3.Therefore,P(rob looses)=2/3
And,P(ben wins)=1/7.Therefore,P(ben looses)=6/7

Putting the values,
6/7.1/4.2/3 + 6/7.3/4.1/3 = 1/7+3/14=5/14

please explain where I am going wrong.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Sep 18, 2009 8:23 pm

uptowngirl92 wrote:P(Mike winning)=P(Ben looses). P(Mike wins) . P(Rob looses)
P(Rob winning)=P(Ben looses). P(Mike looses) . P(Rob wins)

Adding the two will give us the answer right?

Now given,P(mike wins)=1/4.Therefore,P(mike looses)=3/4
Similarly,P(rob wins)=1/3.Therefore,P(rob looses)=2/3
And,P(ben wins)=1/7.Therefore,P(ben looses)=6/7

Putting the values,
6/7.1/4.2/3 + 6/7.3/4.1/3 = 1/7+3/14=5/14

please explain where I am going wrong.

You're double counting losses.

The only conditional part is Ben losing. There's no reason to multiply your individual events by the probability of Rob/Mike losing as well.

So, if you just want to add the two events:

Ben losing then Rob winning = 6/7 * 1/3 = 6/21 = 2/7

Ben losing then Mike winning = 6/7 * 1/4 = 6/28 = 3/14

2/7 + 3/14 = 4/14 + 3/14 = 7/14 = 1/2

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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