Question

A law firm has sixsix senior and sevenseven junior partners. A committee of three partners is selected at random to represent the firm at a conference. What is the probability that at least one of the junior partners is on the​ committee?

Answer 1

Answer:

93.01% probability that at least one of the junior partners is on the​ committee

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the partners are chosen for the committee is not important. This means that we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

What is the probability that at least one of the junior partners is on the​ committee?

Either no junior partners are on the committee, or at least one is. The sum of the probabilities of these events is 100%.

Probability of no junior partners on the commitee:

Desired outcomes:

3 partners from a set of 6(seniors). So

$D = C_{6,3} = \frac{6!}{3!3!} = 20$

Total outcomes:

3 partners from a set of 13(6 seniors, 7 juniors)

$T = C_{13,3} = \frac{13!}{10!3!} = 286$

Probability:

$p = \frac{D}{T} = \frac{20}{286} = 0.0699$

6.99% probability of no juniors partners on the committee

Probability of at least one of the junior partners is on the​ committee:

6.99 + p = 100

p = 93.01

93.01% probability that at least one of the junior partners is on the​ committee

Answer 2

Answer:

0.93 or 93%

Step-by-step explanation:

Junior partners = 7

Senior partners = 6

Total number of partners = 13

The probability that at least one of the junior partners is on the​ three-partners committee is given by 100% minus the probability that no junior partners are on the committee:

$P(X\geq1)=1-P(X=0)\\P(X\geq1)=1 - (\frac{6}{13}*\frac{5}{12}*\frac{4}{11}) \\P(X\geq1)=0.93$

The probability that at least one junior partner is selected is 0.93 or 93%.