Math Problem Statement

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

Solution

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

The sum of all probabilities must be:

P(3)+P(4)+P(5)+P(6)=1P(3) + P(4) + P(5) + P(6) = 1

Substituting the known values:

0.21+P(4)+0.50+0.08=10.21 + P(4) + 0.50 + 0.08 = 1

Simplify the sum of the known probabilities:

0.21+0.50+0.08=0.790.21 + 0.50 + 0.08 = 0.79

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

P(4)+0.79=1P(4) + 0.79 = 1

Subtract 0.79 from both sides:

P(4)=10.79=0.21P(4) = 1 - 0.79 = 0.21

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

P(4)=0.21P(4) = 0.21

Summary:

  • The missing probability P(4)P(4) is 0.210.21.

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.

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Math Problem Analysis

Mathematical Concepts

Probability
Discrete Probability Distribution

Formulas

Sum of probabilities in a discrete distribution: P(3) + P(4) + P(5) + P(6) = 1

Theorems

Sum of Probabilities in a Discrete Distribution Must Equal 1

Suitable Grade Level

Grades 7-10