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solved correctly

by sanju09 » Sat Feb 13, 2010 1:12 am
A GMAT's quant question is given to 3 students who have 1/3, ¼ and ½ chances of solving it correctly. What are the chances that the problem will be solved correctly?
(A) ¼
(B) 1/3
(C) 2/3
(D) ¾
(E) 31/40
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by fibbonnaci » Sat Feb 13, 2010 1:36 am
the question in essence asks us to find the probability of atleast one solving the question correctly.

atleast questions are best answered using the formula:

1- none of them solve the question.

for none to solve the question:it is the prob of 1st person not solving * 2nd person not solving *3rd person not solving.

probability of 1st person not solving = 2/3
2nd person not solving= 3/4
3rd person not solving = 1/2

2/3*3/4*1/2 =>1/4.

1-1/4 => 3/4 => D
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by ajith » Sat Feb 13, 2010 7:07 am
sanju09 wrote:A GMAT's quant question is given to 3 students who have 1/3, ¼ and ½ chances of solving it correctly. What are the chances that the problem will be solved correctly?
(A) ¼
(B) 1/3
(C) 2/3
(D) ¾
(E) 31/40
The probability that each of them solve it wrong = 2/3 , 3/4 and 1/2
Since these are independent events chances of these happening together = 2/3*3/4*1/2 = 1/4

Since the probability that all of them getting it wrong is 1/4, probability that any of them getting it correct is 1-1/4 = 3/4
Always borrow money from a pessimist, he doesn't expect to be paid back.
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