A library has five copies of a certain textbook on reserve of which two copies (1 and 2) are hardcover books and the other three (3, 4, and 5) are softcover books. A student examines these books in random order, stopping only when a softcover book has been selected. One possible outcome is 5, and another is 213. (Enter your answers as a comma-separated list. Enter Ø for the empty set.) Required:
a. List the outcomes in S
b. Let A denote the event that exactly one book must be examined. What outcomes are in A?
c. Let B be the event that book 5 is the one selected. What outcomes are in B?
d. Let C be the event that book 1 is not examined. What outcomes are in C?

Answer and Step-by-step explanation:

(a) Since the student have to stop when he gets to w softcover book, then the sample space should always stop at either 3 or 4 or 5. If the students examines the books randomly and stops at a softcover book, here are the possible ways he could carry this out,

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

2. Since only one book is to be examined then the student must check only one softcover book and end the examining. To do this, either he examines just 3 or 4 or 5. Therefore,

A = {3, 4, 5}

3. We need to pick the possibilities from the sample space that shows that the examining ended at book 5. Therefore,

B = {5, 15, 25, 125, 215}

4. We need to pick possibilities from the sample space that shows that book 1 was not examined. Therefore,

C = {3, 4, 5, 23, 24, 25}

because they could drop even lower..