Question

Angel Sanchez has 8 books on a​ shelf; 5 ​mysteries, 2 science fiction​ books, and 1 biography. Determine the probability of each situation below. ​

(a) Selecting one mystery and then one science fiction​, with replacement
(​b) Selecting one mystery and then one science fiction​, without replacement

Answer 1

a. 5/32

b. 5/28

Step-by-step explanation:

a. Probabilities in First Pick:

Mystery: 5/8

Science: 2/8

Biography: 1/8

Probabilities in Second Pick: Since books are replaced after the first pick, the probabilities will stay the same:

Mystery: 5/8

Science: 2/8

Biography: 1/8

Hence combined probability = 5/8 * 2/8 = 10/64 = 5/32

b. Probabilities in First Pick:

Mystery: 5/8

Science: 2/8

Biography: 1/8

Probabilities in Second Pick: Probabilities will change since books are not being replaced after the first pick

Mystery: 4/7 (Since mystery book is in the first pick, only 4 books will remain)

Science: 2/7

Biography: 1/7

Hence combined probability = 5/8 * 2/7 = 10/56 = 5/28