Math Problem Statement
Solution
To fill in the missing probability, we can use the fact that the sum of all probabilities in a probability distribution must equal 1.
From the table, the given probabilities are:
Let represent the missing probability. The sum of all probabilities must equal 1:
Substitute the known values:
Simplify:
Now solve for :
So, the missing probability .
Would you like further details or have any questions?
Here are 5 related questions to expand your understanding:
- What are the properties of a probability distribution?
- How can you verify if a given set of probabilities forms a valid probability distribution?
- Can probabilities ever be negative or greater than 1?
- How do you interpret the probability of 0.24 for in this context?
- How would you find the expected number of people placed on hold using this probability distribution?
Tip: Always check that the sum of probabilities equals 1 when dealing with probability distributions!
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Math Problem Analysis
Mathematical Concepts
Probability Distribution
Algebra
Formulas
Sum of probabilities: P(0) + P(1) + P(2) + P(3) + P(4) = 1
Theorems
The sum of probabilities in a discrete probability distribution must equal 1.
Suitable Grade Level
Grades 7-10
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