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