https://file.aiquickdraw.com/mathbot/file/1727178670296yjw1nh96.jpg

The problem asks us to find the probability of getting an even number on the 4th roll of a fair six-sided die, given that the first 3 rolls resulted in odd numbers. Let's break down the solution:

1. **Understanding the Die**:
   - A fair six-sided die has the numbers 1, 2, 3, 4, 5, and 6.
   - Odd numbers: 1, 3, 5
   - Even numbers: 2, 4, 6

2. **Probability of Odd or Even Roll**:
   - Probability of rolling an odd number = \(\frac{3}{6} = \frac{1}{2}\)
   - Probability of rolling an even number = \(\frac{3}{6} = \frac{1}{2}\)

3. **Independence of Rolls**:
   - The outcome of the 4th roll is independent of the outcomes of the previous rolls. This means the probability of getting an even number on the 4th roll is not affected by the previous results.

4. **Finding the Required Probability**:
   - Since the probability of rolling an even number on any single roll is \(\frac{1}{2}\), the probability of getting an even number on the 4th roll remains \(\frac{1}{2}\).

Thus, the chance of getting an even number on the 4th throw is:

\[
\text{Probability} = \frac{1}{2}
\]

Would you like more details on this solution or have any additional questions? 

Here are some related questions to consider:
1. What is the probability of getting an odd number on all four rolls?
2. How would the probability change if we used a biased die?
3. What is the probability of getting at least one even number in four rolls?
4. How does the probability change if we roll two six-sided dice together?
5. What is the expected number of even numbers in four rolls?

**Tip:** When dealing with independent events, always remember that the outcome of one event does not affect the outcome of another.

If you get an odd number on each of the first 3 rolls of a fair six-sided dice, find the chance of getting an even number on the 4th throw.

Find the probability of rolling an even number on the 4th throw of a fair six-sided dice, given the first three rolls result in odd numbers. Learn about probability concepts and independent events. Suitable for students in Grades 6-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation