Question

A college library has five copies of a certain text onreserve. Two copies (1 and 2) are first printings, and the other three (3, 4, and 5) are second printings. A student examines these books in random order, stopping only when a second printing has been selected. One possible outcome is 5, and another is 213.

a. List the outcomes in S.

b. Let Adenote the event that exactly one book must be examined. What outcomes are in A?

c. Let Bbe the event that book 5 is the one selected. What outcomes are in B?

d. Let Cbe the event that book 1 is not examined. What outcomes are in C?

Short answer

a. The possible outcomes are,

\(S = \left\{ {\left( 3 \right),\left( 4 \right),\left( 5 \right),\left( {13} \right),\left( {14} \right),\left( {15} \right),\left( {23} \right),\left( {24} \right),\left( {25} \right),\left( {123} \right),\left( {124} \right),\left( {125} \right),\left( {213} \right),\left( {214} \right),\left( {215} \right)} \right\}\)

b. The possible number of outcomes in event A are,

\(A = \left\{ {3,4,5} \right\}\)

c. The possible outcomes in event B are,

\(B = \left\{ {5,15,25,125,215} \right\}\)

d. The possible outcomes in event C are,

\(C = \left\{ {3,4,5,23,25} \right\}\)

Step-by-step solution

Given information

There are 5 copies of a certain text on reserve.

The first printing is two copies (1 and 2) and the second printing are other three copies (3, 4, and 5).

A possible outcome is 5 and another is 213.

List of the possible outcomes in S

a.

Let S represents the sample space.

For the provided scenario, the possible number of outcomes is,

\(S = \left\{ {\left( 3 \right),\left( 4 \right),\left( 5 \right),\left( {13} \right),\left( {14} \right),\left( {15} \right),\left( {23} \right),\left( {24} \right),\left( {25} \right),\left( {123} \right),\left( {124} \right),\left( {125} \right),\left( {213} \right),\left( {214} \right),\left( {215} \right)} \right\}\)

Here, the outcome 123 represents that the 1^st copy of 1^st printing, 2^nd copy of first printing, and 3^rd copy of second printing are examined and then the student stops.

List of the possible outcomes in A

b.

A represents the event that exactly one book must be examined.

The possible number of outcomes in A are,

\(A = \left\{ {3,4,5} \right\}\)

List of the possible outcomes in event B

c.

B represents the event that book 5 is the one selected.

Event B will include all the events where book 5 is selected.

The possible outcomes are,

\(B = \left\{ {5,15,25,125,215} \right\}\)

List of the possible outcomes in event C

d.

C represents the event that book 1 is not examined.

The possible outcomes included in the C are,

\(C = \left\{ {3,4,5,23,25} \right\}\)