Probability

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GaneshMalkar: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Tue Jul 31, 2012 6:53 amFollowed by: 1 member; Thanked: 8 times

by GaneshMalkar » Thu Aug 30, 2012 9:40 am

What is the probability of selecting 1 prime and 3 composite to form a 4 digit code? Prime p = {2} and Composite c = {4,6,8}.

If you cant explain it simply you dont understand it well enough!!!
- Genius

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Source: Beat The GMAT — Problem Solving | Thu Aug 30, 2012 9:40 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 » Thu Aug 30, 2012 10:17 am

Let the 1st digit be prime. Then, the total number of selections = 4*4*3*2
Let the 2nd digit be prime. Then, the total number of selections = 4*4*3*2
Let the 3rd digit be prime. Then, the total number of selections = 4*4*3*2
Let the 4th digit be prime. Then, the total number of selections = 4*4*3*2
Total number of such cases = 4*4*4*3*2

Total number of combinations to form a 4 digit code(If 0 can be placed first and if repetition is not allowed) = 10*9*8*7

Probability = (4*4*4*3*2)/(10*9*8*7) = (4*2)/(5*3*7)= 8/105

p.s: One of the few Probability problems I solved in my life

Anil Gandham
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das.ashmita: Master | Next Rank: 500 Posts; Posts: 118; Joined: Mon May 21, 2012 10:07 pmFollowed by: 4 members; Thanked: 23 times

by das.ashmita » Thu Aug 30, 2012 10:18 pm

Hi Ganesh

Can u please post the OA.

This is how I tried it:

ways of selecting prime = 4C1
ways of selecting composite = 6C3
total ways of selecting any = 10C4

P(Final) = (4C1 * 6C3)/ 10C4 = 8/21

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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 » Fri Aug 31, 2012 5:12 am

GaneshMalkar wrote:What is the probability of selecting 1 prime and 3 composite to form a 4 digit code? Prime p = {2} and Composite c = {4,6,8}.

This question is somewhat ambiguous.
Are you saying that the prime digit must be 2, and that the composite digits must be 4, 6 or 8?

The answer choices would be nice, since some GMAT questions can be solved quickly by first checking the answer choices.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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mohan514: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Wed Feb 08, 2012 8:33 pm; Location: india

by mohan514 » Fri Aug 31, 2012 9:08 am

can anyone explain the question first rather than the answer

though i am not bad with probability
this question didn make sense

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