5. Assuming you toss a fair die once, what is the sample space? Also, find the probability that the number selected is:
5. Assuming you toss a fair die once, what is the sample space? Also, find the probability that the number selected is:
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
Transcribed Image Text:**f) Less than 3 and odd**
**g) Are the events “less than 3” and “odd” mutually exclusive? Explain.**
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In this section, we explore the possibility of a number being both less than 3 and odd, followed by an analysis of whether these two events are mutually exclusive.
**Explanation:**
- **Less than 3 and odd:** A number that meets both conditions is 1, as it is less than 3 and also an odd number.
- **Mutually Exclusive Events:** Two events are mutually exclusive if they cannot occur simultaneously. Here, the event "less than 3" includes the numbers 1 and 2, while "odd" numbers are 1, 3, 5, etc. The existence of the number 1 in both sets indicates that these events are not mutually exclusive.
Through this analysis, students will understand how to determine if events are mutually exclusive and how to identify common elements within different conditions.
Transcribed Image Text:**5. Assuming you toss a fair die once, what is the sample space? Also, find the probability that the number selected is:**
a) Odd (O)
b) Even (E)
c) Less than 3 (L)
d) More than 3 (M)
e) Less than 3 or odd
Expert Solution
Step 1- Writing given data and probability calculation
Given that
A fair dice is rolled.
Sample space = 6 [ Rolling 1 ,2 ,3, 4, 5, 6 ]
We know that
Probability of number selected is
(a) odd (O)
Favorable events = Number of odd numbers in sample space = 3 [ 1 , 3 , 5 ]
Total number of events = Sample space = 6
P(Odd) =
The Probability of number selected is Odd is 0.50
(b) Even
Favorable events = Number of even numbers in sample space = 3 [ 2 , 4 , 6 ]
Total number of events = Sample space = 6
P(Even) =
The Probability that selected number is Even is 0.50
(c) Less than 3
Favorable events = Numbers less than 3 = 2 [ 1 , 2 ]
Total number of events = 6
P(Less than 3) =
The probability that selected number is Less than 3 is 0.3333
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