Two fair 6-sided dice are rolled. Let A = the event that the dice add to 6, and let B = the event that the dice add to an odd number. Find P(A/B) and P(A/B). P(A/B) = (Simplify your answer.) P(AIB') = (Simplify your answer.)
Two fair 6-sided dice are rolled. Let A = the event that the dice add to 6, and let B = the event that the dice add to an odd number. Find P(A/B) and P(A/B). P(A/B) = (Simplify your answer.) P(AIB') = (Simplify your answer.)
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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![**Title: Probability Calculation for Rolling Two Fair 6-Sided Dice**
**Description:**
In this example, we are rolling two fair 6-sided dice and examining two specific events:
- **Event A**: The sum of the numbers on the two dice equals 6.
- **Event B**: The sum of the numbers on the two dice is an odd number.
We aim to find the conditional probability \( P(A|B) \) and the conditional probability \( P(A|B') \), where \( B' \) represents the complement of event B (i.e., the sum of the numbers is not odd, which means it is even).
### Probability Solutions:
**1. Calculate \( P(A|B) \):**
\[ P(A|B) = \text{[Input required]} \]
(Simplify your answer.)
**2. Calculate \( P(A|B') \):**
\[ P(A|B') = \text{[Input required]} \]
(Simplify your answer.)
---
### Explanation:
- **Event A (Sum equals 6)**: Possible pairs (Dice 1, Dice 2) that result in this event are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)
- **Event B (Sum is an odd number)**: Possible pairs (Dice 1, Dice 2) that result in this event include:
- (1, 2), (1, 4), (1, 6)
- (2, 1), (2, 3), (2, 5)
- (3, 2), (3, 4), (3, 6)
- (4, 1), (4, 3), (4, 5)
- (5, 2), (5, 4), (5, 6)
- (6, 1), (6, 3), (6, 5)
- **Event \( B' \) (Sum is an even number)**: All other pairs where the sum is even.
**Note**: Students must find the simplified probabilities by considering the number of favorable outcomes for each event and the relevant conditional probabilities.
**Related Concepts:**
- Basic Probability Rules
- Conditional Probability
- Independent Events](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff138e77-4b21-4b3f-a581-600ea0faba85%2F92b7e301-0be7-43e6-9464-2fd8560b7f20%2F88syqmf_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Probability Calculation for Rolling Two Fair 6-Sided Dice**
**Description:**
In this example, we are rolling two fair 6-sided dice and examining two specific events:
- **Event A**: The sum of the numbers on the two dice equals 6.
- **Event B**: The sum of the numbers on the two dice is an odd number.
We aim to find the conditional probability \( P(A|B) \) and the conditional probability \( P(A|B') \), where \( B' \) represents the complement of event B (i.e., the sum of the numbers is not odd, which means it is even).
### Probability Solutions:
**1. Calculate \( P(A|B) \):**
\[ P(A|B) = \text{[Input required]} \]
(Simplify your answer.)
**2. Calculate \( P(A|B') \):**
\[ P(A|B') = \text{[Input required]} \]
(Simplify your answer.)
---
### Explanation:
- **Event A (Sum equals 6)**: Possible pairs (Dice 1, Dice 2) that result in this event are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)
- **Event B (Sum is an odd number)**: Possible pairs (Dice 1, Dice 2) that result in this event include:
- (1, 2), (1, 4), (1, 6)
- (2, 1), (2, 3), (2, 5)
- (3, 2), (3, 4), (3, 6)
- (4, 1), (4, 3), (4, 5)
- (5, 2), (5, 4), (5, 6)
- (6, 1), (6, 3), (6, 5)
- **Event \( B' \) (Sum is an even number)**: All other pairs where the sum is even.
**Note**: Students must find the simplified probabilities by considering the number of favorable outcomes for each event and the relevant conditional probabilities.
**Related Concepts:**
- Basic Probability Rules
- Conditional Probability
- Independent Events
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