Probability Problem

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frumpychic: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Nov 02, 2011 7:17 am

by frumpychic » Wed Nov 02, 2011 7:23 am

What are the odds of selecting a prime number and an odd number out the set of numbers 1-20 inclusive?

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Source: Beat The GMAT — Problem Solving | Wed Nov 02, 2011 7:23 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Wed Nov 02, 2011 7:28 am

7/20 ?

Anil Gandham
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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Wed Nov 02, 2011 7:38 am

Prime and odd - 3,5,7,11,13,17,19

7/20

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satishchandra: Master | Next Rank: 500 Posts; Posts: 172; Joined: Fri Oct 21, 2011 9:10 pmFollowed by: 2 members; Thanked: 7 times

by satishchandra » Wed Nov 02, 2011 8:12 am

Prime and odd: 3,5,7,11,13,17,19

Probability = 7/20
odds in favor = no.of favorable cases/no.of unfavorable cases= 7/13
odd against = no.of unfavorable cases/no.of favorable cases= 13/7

odds of selecting prime and odd number ~ odds in favor = 7/13
Ans is 7/13
Whats the OA?

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frumpychic: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Nov 02, 2011 7:17 am

by frumpychic » Wed Nov 02, 2011 8:41 am

what about "2"? That is prime but not odd. Do we add that back?

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satishchandra: Master | Next Rank: 500 Posts; Posts: 172; Joined: Fri Oct 21, 2011 9:10 pmFollowed by: 2 members; Thanked: 7 times

by satishchandra » Wed Nov 02, 2011 8:52 am

frumpychic wrote:what about "2"? That is prime but not odd. Do we add that back?

NO. you should not add 2 in your list as it is not odd.

We have the question as prime AND odd (Pay special attention to 'AND' here)
Had it been Prime or odd, then we would have considered all primes and odd numbers in the list.

Whats OA btw?

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studentps2011: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Fri Jul 15, 2011 5:37 am; Thanked: 3 times

by studentps2011 » Wed Nov 02, 2011 12:33 pm

In Gmat questions, is there a differentiation between the terms 'odds' and 'probability' or are they both used to refer to probability?

I have seen probability questions where the term 'odds' is used. At the same time, Kaplan uses them to refer to only 'odds'

For example, in the above question,

odds of selecting prime and odd number = 7/13
whereas,
probability of selecting prime and odd number = 7/20

Experts, advise please!

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GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Wed Nov 02, 2011 12:56 pm

studentps2011 wrote:In Gmat questions, is there a differentiation between the terms 'odds' and 'probability' or are they both used to refer to probability?

I have seen probability questions where the term 'odds' is used. At the same time, Kaplan uses them to refer to only 'odds'

For example, in the above question,

odds of selecting prime and odd number = 7/13
whereas,
probability of selecting prime and odd number = 7/20

Experts, advise please!

I would be extremely surprised if the GMAT ever had a question that tested whether you know the difference between odds and probability. In any case, though, probability is always a number between 0 and 1 that calculates the favorable outcomes divided by the total outcomes. Odds, on the other hand, is the ratio of favorable outcomes to unfavorable outcomes, or unfavorable outcomes to favorable outcomes. For example, if we pick an integer at random from the numbers 1,2,3,4,5. The probability of picking an odd number is 3/5. The odds in FAVOR of picking an odd number are 3:2. The odds AGAINST picking an odd number is 2:3.

Odds and probability are not synonyms, so a real GMAT question would never use the words interchangeably. Any practice question that does is sloppily written.

Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial

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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 » Wed Nov 02, 2011 1:13 pm

studentps2011 wrote:In Gmat questions, is there a differentiation between the terms 'odds' and 'probability' or are they both used to refer to probability?

I have seen probability questions where the term 'odds' is used. At the same time, Kaplan uses them to refer to only 'odds'

For example, in the above question,

odds of selecting prime and odd number = 7/13
whereas,
probability of selecting prime and odd number = 7/20

Experts, advise please!

I agree with GmatMathPro.

I should also add that I don't believe I've ever seen an official GMAT question require us to determine "the odds"

Also, I just checked the OG12 and not one math question asks you to find "the odds."

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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studentps2011: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Fri Jul 15, 2011 5:37 am; Thanked: 3 times

by studentps2011 » Wed Nov 02, 2011 1:20 pm

Thanks Brent & GmatMathPro!

I came across the below problem from Kaplan, which confused me. I could only solve it using probability and then I got the wrong answer!

For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/3, what are the odds of it burning out during the period from 6 months to 1 year following its purchase?

A. 5/27
B. 2/9
C. 1/3
D. 4/9
E. 2/3

OA:D

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