Two fair 4-sided dice are rolled (one red and one green each numbered 1-4). One particular outcome could be (1,4) (red 1, green 4), while another different outcome could be (4,1) (red 4, green 1). Define the following events: • F: at least one of the two dice shows a three • G: the red die shows a number that is bigger than the green die The following are the 16 outcomes in the sample space S. Green 1 3 4 2 (1,1) (1,2) (1,3) (1,4) 1 2 (2,1) (2,2) (2,3) (2,4) Red 3 (3,1) (3,2) (3,3) (3,4) 4 (4,1) (4,2) (4,3) (4,4) For parts (a)-(e), round your answers to 4 decimal places. (a) Find P(F). (b) Find P(G). (c) Find P(F and G).
Two fair 4-sided dice are rolled (one red and one green each numbered 1-4). One particular outcome could be (1,4) (red 1, green 4), while another different outcome could be (4,1) (red 4, green 1). Define the following events: • F: at least one of the two dice shows a three • G: the red die shows a number that is bigger than the green die The following are the 16 outcomes in the sample space S. Green 1 3 4 2 (1,1) (1,2) (1,3) (1,4) 1 2 (2,1) (2,2) (2,3) (2,4) Red 3 (3,1) (3,2) (3,3) (3,4) 4 (4,1) (4,2) (4,3) (4,4) For parts (a)-(e), round your answers to 4 decimal places. (a) Find P(F). (b) Find P(G). (c) Find P(F and G).
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:## Probability and Outcomes in Rolling Two Dice
In this exercise, we will explore the probability associated with the outcomes of rolling two fair 4-sided dice—one red and one green. Each die is numbered from 1 to 4.
### Event Definitions
1. **F**: At least one of the two dice shows a three.
2. **G**: The red die shows a number that is bigger than the green die.
### Sample Space
The 16 possible outcomes when rolling two such dice can be represented as follows:
| | Green 1 | Green 2 | Green 3 | Green 4 |
|---|---------|---------|---------|---------|
| **Red 1** | (1,1) | (1,2) | (1,3) | (1,4) |
| **Red 2** | (2,1) | (2,2) | (2,3) | (2,4) |
| **Red 3** | (3,1) | (3,2) | (3,3) | (3,4) |
| **Red 4** | (4,1) | (4,2) | (4,3) | (4,4) |
### Calculations
For parts (a)-(e), round your answers to 4 decimal places:
**(a) Find P(F).**
**(b) Find P(G).**
**(c) Find P(F and G).**
**(d) Are events F and G disjoint (mutually exclusive)? (yes, no)**
**(e) Find P(F or G).**
**(f) What is the probability that the sum is 3, given that the green die is either 1 or 2?**
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