Question

A college library has five copies of a certain text on reserve. 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 A denote the event that exactly one book must be examined. Whatoutcomes are in A?
C) Let B be the event that book 5 is the one selected. What outcomes arein B?
D) Let C be the event that book 1 is not examined. What outcomes are inC?

Answer 1

Answer:

B) Outcomes in A = {3, 4, 5} .

C) Outcomes in B = {5, 15, 25, 125, 215} .

D) Outcomes in C = {3, 4, 5, 23, 24, 25} .

Step-by-step explanation:

We are given that a college library has five copies of a certain text on reserve. From which two copies (1 and 2) are of first printings, and the other three (3, 4, and 5) are of second printings.

Also, it is stated that a student will stop examining the books only when a second printing has been selected.

A) The outcomes in S are :

      Number of outcomes                                 Selection of Outcomes

                  1                                                                          3

                  2                                                                         4

                  3                                                                          5

                  4                                                                         13

                  5                                                                         14

                  6                                                                         15

                  7                                                                         23

                  8                                                                         24

                  9                                                                         25

                 10                                                                         123

                 11                                                                          124

                 12                                                                          125

                 13                                                                          213

                 14                                                                           214

                 15                                                                            215

Here outcome 123 means 1st copy of first printing is examined then 2nd copy of first printing is examined and then 3rd copy of second printing is examined and then the student stops.

B) A denote the event that exactly one book must be examined.

 So, the outcomes in A will be outcome number 1, 2 and 3 corresponding to selection 3, 4 and 5 of second printing because in these outcomes only one book is examined.

Hence, outcomes in A = {3, 4, 5} .

C) B be the event that book 5 is the one selected. It means all those outcomes in which book 5 was last examined. So, the outcomes in B will be outcome number 3, 6, 9, 12, 15 corresponding to selection 5, 15, 25, 125, 215

Hence, outcomes in B = {5, 15, 25, 125, 215} .

D) C be the event that book 1 is not examined which is outcome number 1, 2, 3, 7, 8, 9 corresponding to selection 3, 4, 5, 23, 24, 25 .

Hence, outcomes in C = {3, 4, 5, 23, 24, 25} .