4. Probability
Multiplication Rule: Dependent Events
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A library has chosen to select the two monthly book club reads by randomly choosing two books from a list of top 100 adult reads posted in the local newspaper. On the list, 62 books are fiction and 38 books are nonfiction. What is the probability of choosing two nonfiction books for this month's book club meeting?
A
0.38
B
0.14
C
0.24
D
0.23
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the probability of selecting two nonfiction books from a list of 100 books, where 62 are fiction and 38 are nonfiction. The selection is random, and no replacement is mentioned, so this is a dependent probability problem.
Step 2: Define the total number of books and the number of nonfiction books. The total number of books is 100, and the number of nonfiction books is 38.
Step 3: Calculate the probability of selecting a nonfiction book on the first draw. This is given by the ratio of nonfiction books to total books: \( P(\text{First Nonfiction}) = \frac{38}{100} \).
Step 4: Calculate the probability of selecting a nonfiction book on the second draw, given that the first book was nonfiction. Since one nonfiction book has already been chosen, there are now 37 nonfiction books left out of a total of 99 books. Thus, \( P(\text{Second Nonfiction | First Nonfiction}) = \frac{37}{99} \).
Step 5: Multiply the probabilities from Step 3 and Step 4 to find the overall probability of selecting two nonfiction books: \( P(\text{Two Nonfiction}) = P(\text{First Nonfiction}) \times P(\text{Second Nonfiction | First Nonfiction}) = \frac{38}{100} \times \frac{37}{99} \). Simplify the expression to get the final probability.
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