An experiment consists of flipping a single coin followed by rolling a six-sided number cube (a die). What is the probability of getting a head followed by an even number?
An experiment consists of flipping a single coin followed by rolling a six-sided number cube (a die). What is the probability of getting a head followed by an even number?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Probability Experiment: Coin Flip and Dice Roll
**Experiment Description:**
The experiment consists of the following steps:
1. **Flipping a Single Coin:** This coin can land on one of two faces - heads (H) or tails (T).
2. **Rolling a Six-Sided Number Cube (a die):** This die has six faces numbered from 1 to 6.
**Question:**
What is the probability of getting a head followed by an even number?
**Solution:**
To determine the probability, we need to consider the two independent events:
1. **Coin Flip Outcome:**
- Probability of getting heads (H): \(\frac{1}{2}\)
- Probability of getting tails (T): \(\frac{1}{2}\)
2. **Dice Roll Outcome:**
- Total outcomes for a six-sided die: 6
- Outcomes resulting in an even number: 2, 4, 6 (3 outcomes)
- Probability of rolling an even number: \(\frac{3}{6} = \frac{1}{2}\)
**Combined Probability:**
Since these events are independent, the combined probability of flipping a head followed by rolling an even number is calculated by multiplying the probabilities of each event:
\[ \text{Probability} = \left( \frac{1}{2} \right) \times \left( \frac{1}{2} \right) = \frac{1}{4} \]
**Interactive Input:**
There is an input textbox followed by a blue "Enter" button where you can practice calculating and submitting the probability.
**Visual Aid:**
A question mark cube graphic is shown to represent the unknown outcome that needs to be solved.
By understanding these steps, students can better grasp the concept of independent events and their combined probabilities in basic probability experiments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c912c6-a327-4873-9511-a364c6ae7474%2Faa8daf87-361a-42b0-85dc-6a74e749ea92%2Fbg83wwq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Experiment: Coin Flip and Dice Roll
**Experiment Description:**
The experiment consists of the following steps:
1. **Flipping a Single Coin:** This coin can land on one of two faces - heads (H) or tails (T).
2. **Rolling a Six-Sided Number Cube (a die):** This die has six faces numbered from 1 to 6.
**Question:**
What is the probability of getting a head followed by an even number?
**Solution:**
To determine the probability, we need to consider the two independent events:
1. **Coin Flip Outcome:**
- Probability of getting heads (H): \(\frac{1}{2}\)
- Probability of getting tails (T): \(\frac{1}{2}\)
2. **Dice Roll Outcome:**
- Total outcomes for a six-sided die: 6
- Outcomes resulting in an even number: 2, 4, 6 (3 outcomes)
- Probability of rolling an even number: \(\frac{3}{6} = \frac{1}{2}\)
**Combined Probability:**
Since these events are independent, the combined probability of flipping a head followed by rolling an even number is calculated by multiplying the probabilities of each event:
\[ \text{Probability} = \left( \frac{1}{2} \right) \times \left( \frac{1}{2} \right) = \frac{1}{4} \]
**Interactive Input:**
There is an input textbox followed by a blue "Enter" button where you can practice calculating and submitting the probability.
**Visual Aid:**
A question mark cube graphic is shown to represent the unknown outcome that needs to be solved.
By understanding these steps, students can better grasp the concept of independent events and their combined probabilities in basic probability experiments.
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