Question 16, 11.5.65
HW Score: $61.11 \%, 11$ of 18
Part 1 of 2
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Angel Sanchez has 8 books on a shelf; 2 mysteries, 5 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
a) The probability of selecting one mystery and then one science fiction, with replacement, is $\square$.
(Type an integer or a simplified fraction.)
Answer
So, the probability of selecting one mystery and then one science fiction, with replacement, is \(\boxed{0.15625}\).
Step 1 ：Angel Sanchez has 8 books on a shelf; 2 mysteries, 5 science fiction books, and 1 biography. We are asked to determine the probability of each situation below.
Step 2 ：First, we are asked to find the probability of selecting one mystery and then one science fiction, with replacement.
Step 3 ：The total number of books is 8, the number of mystery books is 2, and the number of science fiction books is 5.
Step 4 ：The probability of selecting one mystery book is the number of mystery books divided by the total number of books, which is \( \frac{2}{8} = 0.25 \).
Step 5 ：The probability of selecting one science fiction book is the number of science fiction books divided by the total number of books, which is \( \frac{5}{8} = 0.625 \).
Step 6 ：Since the selection is with replacement, the two events are independent. Therefore, the probability of both events happening is the product of their individual probabilities, which is \( 0.25 \times 0.625 = 0.15625 \).
Step 7 ：So, the probability of selecting one mystery and then one science fiction, with replacement, is \(\boxed{0.15625}\).
