smartass666 wrote:

Attorneys are questioning 11 potential jurors about their ability to serve on a jury and decide a case fairly. Seven individuals will be selected to serve on the jury. If each potential juror has an equal chance of being selected, what is the probability that Tamara and Inga are chosen for the jury?

2/11

2/7

21/55

4/11

34/55

A direct probabilistic approach:

First person to be chosen one of the two girls - 2/11

Second person to be chosen to be the other girl - 1/10

The probability to chose both girls - (2/11)*(1/10) = 1/55.

The two girls can be chosen anywhere in the list of the 7 jurors, therefore the final probability is (1/55)*7C2 = (1/55)*(7*6/2) = 21/55.

Combinatorial approach:

Total number of possibilities to choose the 7 jurors - 11C7 = 11*10*9*8/(2*3*4) = 11*10*3.

Number of possibilities to have the two girls among the final 7 jurors - 9C5 = 9*8*7*6/(2*3*4) = 9*2*7 (the two girls must be in, therefore we need to choose 5 more people from the remaining 9).

Required probability 9*2*7/(11*10*3) = 21/55.

(I prefer not to multiply before I express the final probability as a ratio, I always try to reduce a fraction whenever possible.)

Answer C.

_________________

PhD in Applied Mathematics

Love GMAT Quant questions and running.