Question

You get called for Jury duty. There are 100 potential jurors and the judge needs to select twelve of them. Assume the jury is chosen at random.

(a) How many different juries can the judge make from that group?

(b) How many different juries can the judge make which include you?

(c) What is the probability that you will end up on the jury?

Answer 1

You get called for Jury duty. There are 100 potential jurors and the judge needs to select twelve of them. Assume the jury is chosen at random.

a) Now we want to find the number of different juries that can make by the judge.

From 100 potential jurors 12 potential jurors can be selected in ways.

Answer:- The judge can make different juries.

b) Now we want to find the number of different juries that can make by the judge including you. i.e. in the group you are fixed so rest of 11 potential jurors can be selected from 99 potential jurors.

From 99 potential jurors 11 potential jurors can be selected in ways.

Answer:- The judge can make different juries including you.

c) Now we want to find the probability that you will end up on the jury.

[ Note:- According to the classical definition of probability of a event A is defined as,

P(A)= (Number of outcomes favourable to the event A / Number of outcomes in the sample space ) ]

J = Event denoting that you will end up on the jury. So we want to find P(J) .

i.e. P(J)= (Number of outcomes favourable to the event J / Number of outcomes in the sample space )

Here,

=> Number of outcomes favourable to the event J

=> Number of juries including You

and,

=> Number of outcomes in the sample space

=> Number of juries make by judge

Calculation of Probability:

Answer:- Probability that you will end up on the jury is 0.12