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 occurs after the first book is chosen.
Step 2: Recall the formula for probability without replacement. The probability of two events occurring consecutively without replacement is the product of the probabilities of each event. For this problem, the probability of selecting two nonfiction books is: P(A and B) = P(A) × P(B|A), where P(A) is the probability of selecting a nonfiction book on the first draw, and P(B|A) is the probability of selecting a nonfiction book on the second draw given that the first book was nonfiction.
Step 3: Calculate P(A). The probability of selecting a nonfiction book on the first draw is the number of nonfiction books divided by the total number of books: P(A) = 38/100.
Step 4: Calculate P(B|A). After one nonfiction book is selected, there are 37 nonfiction books left and 99 books total. Thus, P(B|A) = 37/99.
Step 5: Multiply the probabilities. To find the overall probability of selecting two nonfiction books, multiply P(A) and P(B|A): P(A and B) = (38/100) × (37/99). Simplify the expression to get the final probability.
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