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In a certain lottery, the probability that a number between 12 and 20,

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In a certain lottery, the probability that a number between 12 and 20,  [#permalink]

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New post 13 Apr 2015, 09:13
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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
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Re: In a certain lottery, the probability that a number between 12 and 20,  [#permalink]

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New post 13 Apr 2015, 09:40
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Titir wrote:
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


Total numbers in lottery = 54
1/3 rd are less than 12 . i.e 18 are less than 12.
So total numbers less than or equal to 20 are 18 + 9 (12 to 20 including )

27/54 answer 1/2
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Re: In a certain lottery, the probability that a number between 12 and 20,  [#permalink]

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New post 24 Jun 2015, 06:57
Titir wrote:
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


Total numbers between 12 and 20 including both = 9
and the probability that a number between 12 and 20, inclusive, is drawn is 1/6

Let X be the total number of lottery
\frac{9}{X} = \frac{1}{6}
Hence X = total number of lottery = 54.

the probability that a number 12 or larger is drawn = 2/3
Hence Number of lottery more than 12 = \frac{(2*54)}{3} = 36
Hence Number of Lottery below 12 = 54-36 = 18
Number of lotteries below 20 (including 20) = 18 + 9 = 27

hence Required probability = Number of lotteries below 20 (including 20) / the total number of lottery = 27/54 = 1/2
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Re: In a certain lottery, the probability that a number between 12 and 20,  [#permalink]

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New post 24 Jun 2015, 21:44
Titir wrote:
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


You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.

Set 1: Number 12 or larger
Set 2: Number 20 or smaller

1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either "12 or more" OR "20 or less" OR both)
2/3 + P(Set 2) - 1/6 = 1
P(Set 2) = 1/2

Answer (D)
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Re: In a certain lottery, the probability that a number between 12 and 20,  [#permalink]

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New post 24 Jun 2015, 22:10
VeritasPrepKarishma wrote:
Titir wrote:
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


You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.

Set 1: Number 12 or larger
Set 2: Number 20 or smaller

1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either "12 or more" OR "20 or less" OR both)
2/3 + P(Set 2) - 1/6 = 1
P(Set 2) = 1/2

Answer (D)


VeritasPrepKarishma

Wow excellent explanation. thanks ... Will try to use your method if i encounter similar question anywhere :)
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Re: In a certain lottery, the probability that a number between 12 and 20,  [#permalink]

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New post 24 Jun 2015, 22:15
If 2/3 of the numbers are at least 12, and 1/6 of the numbers are between 12 and 20 inclusive, then 2/3 - 1/6 = 1/2 of all the numbers are strictly greater than 20. So 1/2 of the numbers must also be 20 or less, which is what the question is asking us to find.
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Re: In a certain lottery, the probability that a number between 12 and 20,   [#permalink] 24 Jun 2015, 22:15
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