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)
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Chapter1: Combinatorial Analysis
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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 \( \frac{3}{4} \).
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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