Another Probability

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amisahoo: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Mon Oct 19, 2009 12:41 am

by amisahoo » Mon Apr 18, 2011 10:02 am

A letter is randomly select from the word studious. What is the probability that the letter be a U?

A. 1/8
B. 1/4
C. 1/3
D. 1/2
E. 3/8

How selecting a U will be 2 different ways and not one . I still doubt the answer

Ans. is : B

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Source: Beat The GMAT — Problem Solving | Mon Apr 18, 2011 10:02 am

manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Mon Apr 18, 2011 10:28 am

amisahoo wrote:A letter is randomly select from the word studious. What is the probability that the letter be a U?

A. 1/8
B. 1/4
C. 1/3
D. 1/2
E. 3/8

How selecting a U will be 2 different ways and not one . I still doubt the answer

Ans. is : B

word studious contain, 2s, 2u, t, d, i, o,.. of these 8 letters, any one letter can be selected in 8C1 ways,..!!

now we have 2u available, with us, therefore no. of ways of selection=2;
hence required probability = 2/8=1/4;

to understand it in a better way, consider studious as a set of words which contains following words {s,s,u,u,d,t,i,o}...!!!

i hope it helps...!!!

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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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 » Mon Apr 18, 2011 10:29 am

amisahoo wrote:A letter is randomly select from the word studious. What is the probability that the letter be a U?

A. 1/8
B. 1/4
C. 1/3
D. 1/2
E. 3/8

How selecting a U will be 2 different ways and not one . I still doubt the answer

Ans. is : B

P = (favorable outcomes)/(total possible outcomes)

Since there are 2 U'2, favorable outcomes = 2.
Since there are 8 letters, total possible outcomes = 8.

P(U) = 2/8 = 1/4.

The correct answer is B.

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