The outcomes of an experiment and the probability of each outcome are given in the table below.

OutcomeProbability

5

0.5

6

0.24

7

0.1

8

0.08

9

0.06

10

0.02

The table shows the outcomes of an experiment and their associated probabilities. Let's summarize this data for clarity:

| Outcome | Probability |
|---------|-------------|
| 5       | 0.5         |
| 6       | 0.24        |
| 7       | 0.1         |
| 8       | 0.08        |
| 9       | 0.06        |
| 10      | 0.02        |

To confirm this represents a valid probability distribution, let's check that the probabilities sum to 1.

\[
0.5 + 0.24 + 0.1 + 0.08 + 0.06 + 0.02 = 1
\]

This distribution is indeed valid as the probabilities add up to 1. Let me know if you need further analysis, like calculating the expected value, variance, or other statistics based on this distribution.

Would you like further details on this, or do you have any specific questions?

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Here are 5 questions that expand on this concept:

1. How do you calculate the expected value (mean) of this probability distribution?
2. What steps are involved in calculating the variance of this distribution?
3. How would you interpret the expected value of this distribution in the context of an experiment?
4. How does knowing the variance help in understanding the spread of outcomes?
5. What does it mean for a probability distribution to be "valid," and how is this checked?

**Tip:** When working with probability distributions, summing probabilities to check for a valid distribution is a crucial first step.

The outcomes of an experiment and the probability of each outcome are given in the table below.

Outcome Probability

5 0.5

6 0.24

7 0.1

8 0.08

9 0.06

10 0.02

Explore probability distributions with an experiment outcome table, including probabilities for each outcome (5 to 10). Learn to validate this probability distribution and understand key concepts like expected value and variance. Suitable for students in Grades 10-12.

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