ch spinner is spun once. 1 1/12 B 4. 4. 2 C B 1/6 nat is the probability of spinning a B then an even number? 1/24 1/3

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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**Probability of Spinning a B then an Even Number**

**Each spinner is spun once.**

Two diagrams representing spinners are shown:

1. The first spinner is divided into four equal sections labeled: A, B, C, and B.
2. The second spinner is divided into four equal sections labeled with the numbers: 1, 2, 3, and 4.

**Question:** What is the probability of spinning a B then an even number?

Four multiple-choice options are provided:

- \(\bigcirc\) 1/12
- \(\bigcirc\) 1/6
- \(\bigcirc\) 1/24
- \(\bigcirc\) 1/3

**Analyzing the problem:**

To calculate the probability, we need to perform two separate events:

1. The probability of spinning a B on the first spinner.
2. The probability of spinning an even number on the second spinner.

**Step-by-Step Explanation:**

1. **Probability of spinning a B on the first spinner:**

   The first spinner has four sections: A, B, C, and B. Out of these sections, B appears twice.
   Probability(B) = Number of B sections / Total sections = 2/4 = 1/2

2. **Probability of spinning an even number on the second spinner:**

   The second spinner has four sections labeled with numbers: 1, 2, 3, and 4. Out of these, 2 and 4 are even numbers.
   Probability(Even Number) = Number of even sections / Total sections = 2/4 = 1/2

Since the events are independent, we multiply the probabilities:

   Probability(B and then an Even Number) = Probability(B) * Probability(Even Number)
                                          = (1/2) * (1/2)
                                          = 1/4

**Therefore, the correct answer is not listed among the provided options, indicating either a mistake in the problem or an omission. However, based on calculations, the closest expected answer should be 1/4.**
Transcribed Image Text:**Probability of Spinning a B then an Even Number** **Each spinner is spun once.** Two diagrams representing spinners are shown: 1. The first spinner is divided into four equal sections labeled: A, B, C, and B. 2. The second spinner is divided into four equal sections labeled with the numbers: 1, 2, 3, and 4. **Question:** What is the probability of spinning a B then an even number? Four multiple-choice options are provided: - \(\bigcirc\) 1/12 - \(\bigcirc\) 1/6 - \(\bigcirc\) 1/24 - \(\bigcirc\) 1/3 **Analyzing the problem:** To calculate the probability, we need to perform two separate events: 1. The probability of spinning a B on the first spinner. 2. The probability of spinning an even number on the second spinner. **Step-by-Step Explanation:** 1. **Probability of spinning a B on the first spinner:** The first spinner has four sections: A, B, C, and B. Out of these sections, B appears twice. Probability(B) = Number of B sections / Total sections = 2/4 = 1/2 2. **Probability of spinning an even number on the second spinner:** The second spinner has four sections labeled with numbers: 1, 2, 3, and 4. Out of these, 2 and 4 are even numbers. Probability(Even Number) = Number of even sections / Total sections = 2/4 = 1/2 Since the events are independent, we multiply the probabilities: Probability(B and then an Even Number) = Probability(B) * Probability(Even Number) = (1/2) * (1/2) = 1/4 **Therefore, the correct answer is not listed among the provided options, indicating either a mistake in the problem or an omission. However, based on calculations, the closest expected answer should be 1/4.**
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