Probability of Picking a Reference Book and Then a Nonfiction Book

Oct 13, 2025 by miodeya.com 4 views

Probability of Picking a Reference Book and Then a Nonfiction Book

Understanding the Problem

In this problem, we are given that Nadia's bookshelf contains 10 fiction books, 2 reference books, and 5 nonfiction books. We need to find the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book.

Step 1: Calculate the Probability of Picking a Reference Book

To calculate the probability of picking a reference book, we need to divide the number of reference books by the total number of books.

There are 2 reference books and a total of 17 books (10 fiction + 2 reference + 5 nonfiction).

So, the probability of picking a reference book is:

P(reference) = Number of reference books / Total number of books = 2 / 17

Step 2: Calculate the Probability of Picking a Nonfiction Book After Picking a Reference Book

Since the reference book is not replaced, the total number of books remaining is 16 (17 - 1).

There are 5 nonfiction books.

So, the probability of picking a nonfiction book after picking a reference book is:

P(nonfiction | reference) = Number of nonfiction books / Total number of books remaining = 5 / 16

Step 3: Calculate the Overall Probability

To calculate the overall probability of picking a reference book and then a nonfiction book, we need to multiply the probabilities calculated in Step 1 and Step 2.

P(reference and nonfiction) = P(reference) × P(nonfiction | reference) = (2 / 17) × (5 / 16) = 10 / 272

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.

P(reference and nonfiction) = 10 / 272 = 5 / 136

Conclusion

The probability that Nadia randomly picks up a reference book and then, without replacing it, picks up a nonfiction book is 5/136, which can be simplified to 1/27.2 or approximately 0.0367.

Therefore, the correct answer is:

A. $\frac{1}{289}$ is incorrect, the correct answer is $\frac{1}{27.2}$
Frequently Asked Questions (FAQs) About Probability of Picking a Reference Book and Then a Nonfiction Book

Q: What is the probability of picking a reference book from Nadia's bookshelf?

A: The probability of picking a reference book is 2/17, since there are 2 reference books out of a total of 17 books.

Q: What is the probability of picking a nonfiction book after picking a reference book?

A: The probability of picking a nonfiction book after picking a reference book is 5/16, since there are 5 nonfiction books out of a total of 16 books remaining after the reference book is picked.

Q: How do I calculate the overall probability of picking a reference book and then a nonfiction book?

A: To calculate the overall probability, you need to multiply the probabilities of picking a reference book and then a nonfiction book. The formula is:

P(reference and nonfiction) = P(reference) × P(nonfiction | reference)

Q: What is the overall probability of picking a reference book and then a nonfiction book?

A: The overall probability of picking a reference book and then a nonfiction book is 10/272, which can be simplified to 5/136.

Q: Why is the probability of picking a reference book and then a nonfiction book not 1/17 × 5/16?

A: The probability of picking a reference book and then a nonfiction book is not 1/17 × 5/16 because the total number of books remaining after the reference book is picked is 16, not 17.

Q: Can I use a calculator to calculate the probability?

A: Yes, you can use a calculator to calculate the probability. Simply enter the numbers and the calculator will give you the result.

Q: What is the significance of this problem?

A: This problem is significant because it illustrates the concept of conditional probability, which is an important concept in probability theory. It also shows how to calculate the probability of two events occurring in sequence.

Q: Can I apply this concept to real-life situations?

A: Yes, you can apply this concept to real-life situations where you need to calculate the probability of two events occurring in sequence. For example, in a game of chance, you may need to calculate the probability of drawing a certain card from a deck and then drawing another card.

Q: What are some common mistakes to avoid when calculating probability?

A: Some common mistakes to avoid when calculating probability include:

Not considering the total number of outcomes
Not considering the probability of each event
Not multiplying the probabilities of each event
Not simplifying the fraction

By avoiding these common mistakes, you can ensure that your calculations are accurate and reliable.