plece of frui ou then return it, and select a different piece of fruit. Find the probability that you elect an apple and a peach.
plece of frui ou then return it, and select a different piece of fruit. Find the probability that you elect an apple and a peach.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Which one is right
![**Problem Statement:**
A basket contains six apples and five peaches. You randomly select one piece of fruit. You then return it and select a different piece of fruit. Find the probability that you select an apple and a peach.
**Explanation:**
We need to find the probability that when a fruit is selected randomly twice from the basket, the first fruit is an apple and the second fruit is a peach. Here are the steps to solve this:
1. **Calculate the total number of fruits:**
There are 6 apples and 5 peaches, so the total number of fruits is:
\[
6 + 5 = 11
\]
2. **Probability of selecting an apple first:**
The probability of selecting an apple in the first draw is the number of apples divided by the total number of fruits:
\[
\frac{6}{11}
\]
3. **Probability of selecting a peach second:**
Since the fruit is returned to the basket, the total number of fruits remains the same (11). Therefore, the probability of selecting a peach in the second draw is the number of peaches divided by the total number of fruits:
\[
\frac{5}{11}
\]
4. **Combined probability:**
Since the draws are independent (because the fruit is returned to the basket after the first draw), we can multiply the probabilities of the two independent events:
\[
\frac{6}{11} \times \frac{5}{11} = \frac{30}{121}
\]
So, the probability that you select an apple first and a peach second is \( \frac{30}{121} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfd2fdb4-ed37-4589-bb6e-71b3bbd6ec92%2F667b7405-8b72-4f2e-b1cd-5448c582417f%2Ffokrk8i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A basket contains six apples and five peaches. You randomly select one piece of fruit. You then return it and select a different piece of fruit. Find the probability that you select an apple and a peach.
**Explanation:**
We need to find the probability that when a fruit is selected randomly twice from the basket, the first fruit is an apple and the second fruit is a peach. Here are the steps to solve this:
1. **Calculate the total number of fruits:**
There are 6 apples and 5 peaches, so the total number of fruits is:
\[
6 + 5 = 11
\]
2. **Probability of selecting an apple first:**
The probability of selecting an apple in the first draw is the number of apples divided by the total number of fruits:
\[
\frac{6}{11}
\]
3. **Probability of selecting a peach second:**
Since the fruit is returned to the basket, the total number of fruits remains the same (11). Therefore, the probability of selecting a peach in the second draw is the number of peaches divided by the total number of fruits:
\[
\frac{5}{11}
\]
4. **Combined probability:**
Since the draws are independent (because the fruit is returned to the basket after the first draw), we can multiply the probabilities of the two independent events:
\[
\frac{6}{11} \times \frac{5}{11} = \frac{30}{121}
\]
So, the probability that you select an apple first and a peach second is \( \frac{30}{121} \).
Transcribed Image Text:Below are the fractions as displayed in the image:
- 30/121
- 1/4
- 25/121
- 36/121
There are no graphs or diagrams in the image.
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