0000 0000 The numbered disks shown are placed in a box and one disk is selected at random. Find the probability of selecting an odd number, given that a green disk is selected. green blue green green green blue green blue Find the probability of selecting an odd number, given that a green disk is selected. (Type an integer or a simplified fraction.)
0000 0000 The numbered disks shown are placed in a box and one disk is selected at random. Find the probability of selecting an odd number, given that a green disk is selected. green blue green green green blue green blue Find the probability of selecting an odd number, given that a green disk is selected. (Type an integer or a simplified fraction.)
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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![The problem at hand involves selecting a disk from a set of disks, each uniquely numbered and colored either green or blue. The goal is to determine the probability of selecting a disk with an odd number, given that a green disk is selected.
### Disk Arrangement:
- Disks 1, 3, 5, and 7 are colored green.
- Disks 2, 4, 6, and 8 are colored blue.
### Analysis:
- **Total Green Disks:** 4 (Numbered 1, 3, 5, 7)
- **Green Disks with Odd Numbers:** 3 (Numbered 1, 3, 5)
### Probability Calculation:
To find the probability of selecting an odd number given that a green disk is selected, we use the following approach:
1. Identify the favorable outcomes (green disks with odd numbers): 3 (1, 3, 5).
2. Determine the total number of possible outcomes (total green disks): 4 (1, 3, 5, 7).
The probability is then calculated as the ratio of favorable outcomes to total outcomes:
\[
\text{Probability} = \frac{\text{Number of Green Disks with Odd Numbers}}{\text{Total Number of Green Disks}} = \frac{3}{4}
\]
Therefore, the probability of selecting an odd number, given that a green disk is selected, is \( \frac{3}{4} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb035bd8-242a-4bd8-91c3-9303fe022dfd%2Ffe4be106-0404-46c0-95ae-b84ee8ad6d25%2F109e3wl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem at hand involves selecting a disk from a set of disks, each uniquely numbered and colored either green or blue. The goal is to determine the probability of selecting a disk with an odd number, given that a green disk is selected.
### Disk Arrangement:
- Disks 1, 3, 5, and 7 are colored green.
- Disks 2, 4, 6, and 8 are colored blue.
### Analysis:
- **Total Green Disks:** 4 (Numbered 1, 3, 5, 7)
- **Green Disks with Odd Numbers:** 3 (Numbered 1, 3, 5)
### Probability Calculation:
To find the probability of selecting an odd number given that a green disk is selected, we use the following approach:
1. Identify the favorable outcomes (green disks with odd numbers): 3 (1, 3, 5).
2. Determine the total number of possible outcomes (total green disks): 4 (1, 3, 5, 7).
The probability is then calculated as the ratio of favorable outcomes to total outcomes:
\[
\text{Probability} = \frac{\text{Number of Green Disks with Odd Numbers}}{\text{Total Number of Green Disks}} = \frac{3}{4}
\]
Therefore, the probability of selecting an odd number, given that a green disk is selected, is \( \frac{3}{4} \).
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