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:
- (This is what we need to find)
The sum of all probabilities must be:
Substituting the known values:
Simplify the sum of the known probabilities:
Now, set up the equation to solve for :
Subtract 0.79 from both sides:
So, the required value of the missing probability is:
Summary:
- The missing probability is .
Do you need any further clarification or details?
Here are some related questions to expand on this:
- How can we verify if a given set of probabilities represents a valid probability distribution?
- What are the properties of a discrete probability distribution?
- How would you determine if a probability distribution is uniform?
- What is the difference between a discrete and a continuous probability distribution?
- 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
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