An experiment consists of first rolling a die and then tossing a coin: a. How many elements are there in the sample space? \[ \text{Sample space size:} \, \_\_\_\_ \] b. Let \( A \) be the event that either a 3 or 4 is rolled first, followed by landing a head on the coin toss. \[ P(A) = \_\_ \] Present your answer as a decimal rounded to four decimal places. c. Let \( B \) be the event that a number less than 3 is rolled, followed by landing a head on the coin toss. Are the events \( A \) and \( B \) mutually exclusive? \[ \begin{array}{c} \text{O No, they are not Mutually Exclusive} \\ \text{O Yes, they are Mutually Exclusive} \end{array} \] **Hint:** Mutually Exclusive [Video on Probability](#) [Submit All Parts]
An experiment consists of first rolling a die and then tossing a coin: a. How many elements are there in the sample space? \[ \text{Sample space size:} \, \_\_\_\_ \] b. Let \( A \) be the event that either a 3 or 4 is rolled first, followed by landing a head on the coin toss. \[ P(A) = \_\_ \] Present your answer as a decimal rounded to four decimal places. c. Let \( B \) be the event that a number less than 3 is rolled, followed by landing a head on the coin toss. Are the events \( A \) and \( B \) mutually exclusive? \[ \begin{array}{c} \text{O No, they are not Mutually Exclusive} \\ \text{O Yes, they are Mutually Exclusive} \end{array} \] **Hint:** Mutually Exclusive [Video on Probability](#) [Submit All Parts]
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![An experiment consists of first rolling a die and then tossing a coin:
a. How many elements are there in the sample space?
\[ \text{Sample space size:} \, \_\_\_\_ \]
b. Let \( A \) be the event that either a 3 or 4 is rolled first, followed by landing a head on the coin toss.
\[ P(A) = \_\_ \]
Present your answer as a decimal rounded to four decimal places.
c. Let \( B \) be the event that a number less than 3 is rolled, followed by landing a head on the coin toss. Are the events \( A \) and \( B \) mutually exclusive?
\[ \begin{array}{c}
\text{O No, they are not Mutually Exclusive} \\
\text{O Yes, they are Mutually Exclusive}
\end{array} \]
**Hint:** Mutually Exclusive
[Video on Probability](#)
[Submit All Parts]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F989f3804-21ca-49de-b68d-d803cbef5906%2F418eca90-e2a6-4210-8bde-9017cad3a46e%2Fh0ph8b.jpeg&w=3840&q=75)
Transcribed Image Text:An experiment consists of first rolling a die and then tossing a coin:
a. How many elements are there in the sample space?
\[ \text{Sample space size:} \, \_\_\_\_ \]
b. Let \( A \) be the event that either a 3 or 4 is rolled first, followed by landing a head on the coin toss.
\[ P(A) = \_\_ \]
Present your answer as a decimal rounded to four decimal places.
c. Let \( B \) be the event that a number less than 3 is rolled, followed by landing a head on the coin toss. Are the events \( A \) and \( B \) mutually exclusive?
\[ \begin{array}{c}
\text{O No, they are not Mutually Exclusive} \\
\text{O Yes, they are Mutually Exclusive}
\end{array} \]
**Hint:** Mutually Exclusive
[Video on Probability](#)
[Submit All Parts]
Expert Solution
Step 1
Given:
First, a die is rolled.
Second, a coin is tossed.
Number of sides in a die = 6
Both sides of a coin is equally likely.
Step 2
a)
Sample space consists of the following outcomes.
(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)
Number of elements = 12
b)
Number of outcomes in events A = (3,H), (4,H) = 2
So,
The answer is 0.1667
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