Determine the required value of the missing probability to make the distribution a discrete probability distribution.  x	P(x)

3	0.21

4	?

5	0.50

6	0.08

To determine the required value of the missing probability in a discrete probability distribution, we need to remember that the sum of all probabilities in a valid probability distribution must equal 1.

We have:

- \( P(3) = 0.21 \)
- \( P(4) = ? \) (This is what we need to find)
- \( P(5) = 0.50 \)
- \( P(6) = 0.08 \)

The sum of all probabilities must be:

\[
P(3) + P(4) + P(5) + P(6) = 1
\]

Substituting the known values:

\[
0.21 + P(4) + 0.50 + 0.08 = 1
\]

Simplify the sum of the known probabilities:

\[
0.21 + 0.50 + 0.08 = 0.79
\]

Now, set up the equation to solve for \( P(4) \):

\[
P(4) + 0.79 = 1
\]

Subtract 0.79 from both sides:

\[
P(4) = 1 - 0.79 = 0.21
\]

So, the required value of the missing probability \( P(4) \) is:

\[
P(4) = 0.21
\]

### Summary:
- The missing probability \( P(4) \) is \( 0.21 \).

Do you need any further clarification or details?

Here are some related questions to expand on this:

1. How can we verify if a given set of probabilities represents a valid probability distribution?
2. What are the properties of a discrete probability distribution?
3. How would you determine if a probability distribution is uniform?
4. What is the difference between a discrete and a continuous probability distribution?
5. How would the distribution change if we added another outcome with a probability of 0.1?

**Tip**: Remember, the sum of all probabilities in a discrete probability distribution must always equal 1. This is a key feature of any valid probability model.

Determine the required value of the missing probability to make the distribution a discrete probability distribution. x P(x): 3 - 0.21, 4 - ?, 5 - 0.50, 6 - 0.08

Learn how to find the missing probability in a discrete probability distribution where the sum of all probabilities must equal 1. In this problem, given probabilities for x = 3, 5, and 6, the missing probability for x = 4 is calculated step by step. Suitable for Grades 7-10.

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