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by maihuna » Tue Mar 15, 2011 12:12 pm
In a certain lottery, the probability that a number between 12
and 20, inclusive, is drawn is 1
6 . If the probability that a
number 12 or larger is drawn is 2
3 , what is the probability
that a number less than or equal to 20 is drawn?
(A) 1
18
(B) 1
6
(C) 1
3
(D) 1
2
(E) 5
6
Charged up again to beat the beast :)
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by force5 » Tue Mar 15, 2011 1:55 pm
please check the question.. its not making sense.... some symbols are missing somewhere... its that 1/6 and 2/3 or what??
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by Stuart@KaplanGMAT » Tue Mar 15, 2011 2:09 pm
maihuna wrote:In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1 in 6 . If the probability that a number 12 or larger is drawn is 2 in 3, what is the probability that a number less than or equal to 20 is drawn?

(A) 1/18
(B) 1/6
(C) 1/3
(D) 1/2
(E) 5/6
I fixed the question - please always preview your posts to make sure that they're readable!

This is a simple question to solve once you've broken it down, so let's get to breaking!

If the probability of 12 or larger is 2/3 and the probability of 12-20 is 1/6, then we can set up and solve the following equation:

Prob(12+) = Prob(12-20) + Prob(21+)
2/3 = 1/6 + Prob(21+)
2/3 - 1/6 = Prob(21+)
4/6 - 1/6 = Prob(21+)
3/6 = 1/2 = Prob(21+)

We can now answer the question by setting up and solving one more equation:

Prob(want) = 1 - Prob(don't want)
Prob(less than or equal to 20) = 1 - Prob(greater than 20)
Prob(less than or equal to 20) = 1 - 1/2 = 1/2

choose (D)!
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