Consider the probability experiment in which a 4-side dice is tossed twice and two coins are tossed. What is the size of the sample space S? |S| =
Consider the probability experiment in which a 4-side dice is tossed twice and two coins are tossed. What is the size of the sample space S? |S| =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![**Sample Space Size**
Consider the probability experiment in which a 4-sided die is tossed twice and two coins are tossed.
What is the size of the sample space \( S \)?
\[ |S| = \]
---
**Explanation:**
To find the size of the sample space, we need to consider all possible outcomes of the experiment.
1. **4-sided die tossed twice**: Each die has 4 possible outcomes. When tossed twice, the total number of outcomes is \( 4 \times 4 = 16 \).
2. **Two coins tossed**: Each coin has 2 possible outcomes (heads or tails). When two coins are tossed, the total number of outcomes is \( 2 \times 2 = 4 \).
The overall size of the sample space \( S \) can be calculated by multiplying the number of outcomes for the dice and the coins:
\[ |S| = 16 \times 4 = 64 \]
Thus, the size of the sample space \( S \) is 64.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd84c1829-b5be-42b1-ba72-3bae7a546286%2F45efee58-3ec6-4ee6-8d54-590a372aeaeb%2F8dhmmcr_processed.png&w=3840&q=75)
Transcribed Image Text:**Sample Space Size**
Consider the probability experiment in which a 4-sided die is tossed twice and two coins are tossed.
What is the size of the sample space \( S \)?
\[ |S| = \]
---
**Explanation:**
To find the size of the sample space, we need to consider all possible outcomes of the experiment.
1. **4-sided die tossed twice**: Each die has 4 possible outcomes. When tossed twice, the total number of outcomes is \( 4 \times 4 = 16 \).
2. **Two coins tossed**: Each coin has 2 possible outcomes (heads or tails). When two coins are tossed, the total number of outcomes is \( 2 \times 2 = 4 \).
The overall size of the sample space \( S \) can be calculated by multiplying the number of outcomes for the dice and the coins:
\[ |S| = 16 \times 4 = 64 \]
Thus, the size of the sample space \( S \) is 64.
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