2/3 ### Probability Theory: Conditional Probability ProblemWhen randomly selecting adults, let $ M $ denote the event of randomly selecting a male and let $ B $ denote the event of randomly selecting someone with blue eyes. #### Problem Statement:What does $ P(M|B) $ represent?#### Answer Options:- $ \text{A.} $ The probability of getting a male, given that someone with blue eyes has been selected.- $ \text{B.} $ The probability of getting a male or getting someone with blue eyes.- $ \text{C.} $ The probability of getting someone with blue eyes, given that a male has been selected.- $ \text{D.} $ The probability of getting a male and getting someone with blue eyes.#### Second Problem Statement:Is $ P(M|B) $ the same as $ P(B|M) $?#### Answer Options:- $ \text{A.} $ No, because $ P(B|M) $ represents the probability of getting a male, given that someone with blue eyes has been selected.- $ \text{B.} $ Yes, because $ P(B|M) $ represents the probability of getting someone with blue eyes, given that a male has been selected.- $ \text{C.} $ Yes, because $ P(B|M) $ represents the probability of getting a male, given that someone with blue eyes has been selected.- $ \text{D.} $ No, because $ P(B|M) $ represents the probability of getting someone with blue eyes, given that a male has been selected.### Explanation of Concepts:- **Conditional Probability $ P(A|B) $**: This represents the probability of event $ A $ occurring given that event $ B $ has already occurred. In general, $ P(A|B) \neq P(B|A) $ because the conditions under which each probability is calculated are different.### Analysis of Answer Choices:#### For the First Problem:- **Correct Answer: $ \text{A.} $** $ P(M|B) $ is the probability of selecting a male given that the person has blue eyes.#### For the Second Problem:- **Correct Answer: $ \text{D.} $** \( P(B|

P(A|B) is the probability of event A occurring, given that event B occurs. let M denote the event…

When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B) the same as P(B|M)? What does P(M|B) represent? O A. The probability of getting a male, given that someone with blue eyes has been selected. O B. The probability of getting a male or getting someone with blue eyes. Oc. The probability of getting someone with blue eyes, given that a male has been selected. O D. The probability of getting a male and getting someone with blue eyes. Is P(M|B) the same as P(B|M)? O A. No, because P(B|M) represents the probability of getting a male, given that someone with blue eyes has been selected. O B. Yes, because P(B|M) represents the probability of getting someone with blue eyes, given that a male has been selected. Oc. Yes, because P(B|M) represents the probability of getting a male, given that someone with blue eyes has been selected. O D. No, because P(B|M) represents the probability of getting someone with blue eyes, given that a male has been selected.

When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B) the same as P(B|M)? What does P(M|B) represent? O A. The probability of getting a male, given that someone with blue eyes has been selected. O B. The probability of getting a male or getting someone with blue eyes. Oc. The probability of getting someone with blue eyes, given that a male has been selected. O D. The probability of getting a male and getting someone with blue eyes. Is P(M|B) the same as P(B|M)? O A. No, because P(B|M) represents the probability of getting a male, given that someone with blue eyes has been selected. O B. Yes, because P(B|M) represents the probability of getting someone with blue eyes, given that a male has been selected. Oc. Yes, because P(B|M) represents the probability of getting a male, given that someone with blue eyes has been selected. O D. No, because P(B|M) represents the probability of getting someone with blue eyes, given that a male has been selected.

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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Question

2/3

### Probability Theory: Conditional Probability Problem

When randomly selecting adults, let $ M $ denote the event of randomly selecting a male and let $ B $ denote the event of randomly selecting someone with blue eyes.

#### Problem Statement:
What does $ P(M|B) $ represent?

#### Answer Options:

- $ \text{A.} $ The probability of getting a male, given that someone with blue eyes has been selected.
- $ \text{B.} $ The probability of getting a male or getting someone with blue eyes.
- $ \text{C.} $ The probability of getting someone with blue eyes, given that a male has been selected.
- $ \text{D.} $ The probability of getting a male and getting someone with blue eyes.

#### Second Problem Statement:
Is $ P(M|B) $ the same as $ P(B|M) $?

#### Answer Options:

- $ \text{A.} $ No, because $ P(B|M) $ represents the probability of getting a male, given that someone with blue eyes has been selected.
- $ \text{B.} $ Yes, because $ P(B|M) $ represents the probability of getting someone with blue eyes, given that a male has been selected.
- $ \text{C.} $ Yes, because $ P(B|M) $ represents the probability of getting a male, given that someone with blue eyes has been selected.
- $ \text{D.} $ No, because $ P(B|M) $ represents the probability of getting someone with blue eyes, given that a male has been selected.

### Explanation of Concepts:

- **Conditional Probability $ P(A|B) $**: This represents the probability of event $ A $ occurring given that event $ B $ has already occurred. In general, $ P(A|B) \neq P(B|A) $ because the conditions under which each probability is calculated are different.

### Analysis of Answer Choices:

#### For the First Problem:

- **Correct Answer: $ \text{A.} $** $ P(M|B) $ is the probability of selecting a male given that the person has blue eyes.

#### For the Second Problem:

- **Correct Answer: $ \text{D.} $** \( P(B|

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