DS on probability question

Answer E

1. More than half the ppl are women

Say Women=6
Probability both are women =6c2/10c2=1/3<1/2
Say Women=9
Probability both are women =9c2/10c2=72/90>1/2
Not Suff

2. Probability of both being men is less than 1/10

Say N.of women=7, Men=3
Probability of both being men = 3c2/10c2=1/15<1/10
Probability of bot being women=7c2/10c2=42/90<1/2

Say N.of women=8, Men=2
Probability of both being men = 2c2/10c2=1/90<1/10
Probability of bot being women=8c2/10c2=56/90>1/2

Not Suff

Both statements not suff.
Answer E

r_walid wrote:If 2 diff. representatives are to be selected from a group of 10 ppl and if p is the probability that both representatives will be women.

is P>1/2



1- More than 1/2 of the 10 employees are women
2- the probability that both representatives will be men is less than 1/10.

rephrase question to is #women > 7 or #men <3?

p>1/2 -> x/10 * (10-x)/9 >1/2 -> x+x^2>45 -> x(x+1)>45 hence x>7

1. # women = 6, 7, 8, 9 or 10 -> insuff
2. tells us # men = 1, 2 or 3 -> insuff

combined insuff since you can have 1 man 9 women which ans yes to the posed question of you can have 3 men andf 7 women which answers no to the posed question.

hope that helps.