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Probability---selection of two representatives

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Probability---selection of two representatives

by prachich1987 » Sat Dec 11, 2010 2:33 am
If 2 different representatives are to be selected at random from a group of 10 employees
and if p is the probability that both representatives selected will be women, is p >0.5

(1) More than 0.5 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 0.1

Mark
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

According to me the answer should be D.In both the cases the probability would be greater than 0.5
But the answer given in the book is E

I WOULD BE GRATEFUL IF SOMEONE CAN EXPLAIN.
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by Rahul@gurome » Sat Dec 11, 2010 7:13 am
prachich1987 wrote:If 2 different representatives are to be selected at random from a group of 10 employees
and if p is the probability that both representatives selected will be women, is p >0.5

(1) More than 0.5 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 0.1
Given: Possible number of way to select 2 out of 10 = 10C2 = 45

Statement 1: More than 1/2 of the 10 employees are women.
Number of can be 6, 7, 8, 9 or 10.
  • For number of women = 6, Possible number of selecting two women out of 6 = 6C2 = 15. Thus probability = 15/45 = 1/3 < 1/2

    For number of women = 9, Possible number of selecting two women out of 9 = 9C2 = 36. Thus probability = 36/45 = 4/5 > 1/2
Not sufficient.

Statement 2: The probability that both representatives selected will be men is less than 0.1. This means (Probability that both representative will be women + Probability that one of the representative will be man and other woman) > (1 - 0.1) = 0.9

But we don't have any idea about "Probability that one of the representative will be man and other woman".

Not sufficient.


1 & 2 Together: No relevant new information.

Not sufficient.

The correct answer is E.
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by shovan85 » Sat Dec 11, 2010 7:14 am
prachich1987 wrote:If 2 different representatives are to be selected at random from a group of 10 employees
and if p is the probability that both representatives selected will be women, is p >0.5

(1) More than 0.5 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 0.1

According to me the answer should be D.In both the cases the probability would be greater than 0.5
But the answer given in the book is E

I WOULD BE GRATEFUL IF SOMEONE CAN EXPLAIN.
Lets say women = W

The probability that both representatives selected will be women
= p = C(W,2) / C(10,2) = C(W,2) / 45

from (A)

W>5

Say W=6
p = C(6,2)/45 = 15/45 = 1/3 which is less than 1/2

Say W=10 then p = 1

As no concrete value of p is found option A is insufficient

from (B)

probability that both representatives selected will be men
= C(M,2)/45

C(M,2)/45 < 1/10
=> C(M,2) < 45/10
=> M * (M-1) < 9

Thus, M <=3 which means women >= 7

when W = 7 then prob for women = C(7,2)/45 = 21/45 < 1/2
when W = 10 then prob for women = C(10,2)/45 = 1 > 1/2

As no concrete value of p is found option B is insufficient.

Combine both no use

Thus E
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