DS Questions on probability

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Tue Jun 21, 2011 11:28 pm

Set S of cardinality 7 has distinct elements. Is the probability of picking out a prime number
from Set S less than 4/5?
(1)The least element and the largest element of Set S are 8 and 18 respectively.
(2)If two prime elements are added into Set S, the probability that a prime number is picked
up from the extended set S is 1/3
(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer tlVe question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

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Source: Beat The GMAT — Data Sufficiency | Tue Jun 21, 2011 11:28 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jun 22, 2011 12:05 am

knight247 wrote:Set S of cardinality 7 has distinct elements. Is the probability of picking out a prime number
from Set S less than 4/5?
(1)The least element and the largest element of Set S are 8 and 18 respectively.
(2)If two prime elements are added into Set S, the probability that a prime number is picked
up from the extended set S is 1/3

Statement 1: Maximum number of prime numbers in the set can be 3 when all the prime numbers between 8 and 18 (i.e. 11, 13, and 17) are in the set.

Hence, maximum probability of picking out a prime number from S = 3/7
As the maximum probability is less than 4/5, the required probability will be always less than 4/5.

Sufficient

Statement 2: Say, the number of prime numbers in S is n. Thus, in the extended set number of elements is (7 + 2) = 9 and number of prime number is (n + 2).

Hence, (n + 2)/9 = 1/3 --> n = 1
Therefore, probability of picking out a prime number from original S = 1/7 < 4/5

Sufficient

The correct answer is D.

Anurag Mairal, Ph.D., MBA
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mirantdon: Master | Next Rank: 500 Posts; Posts: 135; Joined: Thu May 05, 2011 9:00 amFollowed by: 1 member; Thanked: 4 times; GMAT Score:700

by mirantdon » Tue Jun 28, 2011 1:50 am

It was quite straight forward .

imo d

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