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Two fair dice are rolled. What is the probability of the dice being equal? 1) 3/36 2) 4/36 3) 6/36 4) 12/36

Two fair dice are rolled. What is the probability of the dice being equal? 1) 3/36 2) 4/36 3) 6/36 4) 12/36

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Probability of Rolling Equal Numbers with Two Dice When two fair dice are rolled, we are interested in calculating the probability that the numbers on both dice will be equal. The possible outcomes for rolling two dice have the form (a, b) where: - \(a\) is the outcome of the first die (1 through 6). - \(b\) is the outcome of the second die (1 through 6). The total number of possible outcomes when rolling two dice is \(6 \times 6 = 36\). **Question:** Two fair dice are rolled. What is the probability of the dice being equal? **Options:** 1. 3/36 2. 4/36 3. 6/36 4. 12/36 #### Explanation: For the dice to be equal: \[ (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) \] There are exactly 6 possible outcomes where both dice show the same number. **Detailed Calculation:** - Number of favorable outcomes: 6 - Total number of outcomes: 36 The probability is calculated as: \[ P(\text{equal dice}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \] From the provided options, the correct answer is: - Option 3) 6/36
Transcribed Image Text:### Probability of Rolling Equal Numbers with Two Dice When two fair dice are rolled, we are interested in calculating the probability that the numbers on both dice will be equal. The possible outcomes for rolling two dice have the form (a, b) where: - \(a\) is the outcome of the first die (1 through 6). - \(b\) is the outcome of the second die (1 through 6). The total number of possible outcomes when rolling two dice is \(6 \times 6 = 36\). **Question:** Two fair dice are rolled. What is the probability of the dice being equal? **Options:** 1. 3/36 2. 4/36 3. 6/36 4. 12/36 #### Explanation: For the dice to be equal: \[ (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) \] There are exactly 6 possible outcomes where both dice show the same number. **Detailed Calculation:** - Number of favorable outcomes: 6 - Total number of outcomes: 36 The probability is calculated as: \[ P(\text{equal dice}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \] From the provided options, the correct answer is: - Option 3) 6/36
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