The sum of the probabilities in a uniform probability distribution is 1.
Hence, option C is the right choice.
What is a uniform probability distribution?
A uniform distribution is a probability distribution in which all events have the same probability.
Because the chances of drawing a heart, a club, a diamond, or a spade are equal, a deck of cards has uniform distributions.
How do we solve the given question?
The general formula for the probability density function (pdf) for the uniform distribution is: f(x) = 1/ (b - a) for a ≤ x ≤ b.
To find the sum of all the probabilities in a uniform probability distribution, we do the integral over f(x).
[tex]\therefore SUM = \int_{a}^{b}f(x)dx\\or, SUM = \int_{a}^{b}\frac{1}{b-a}dx\\or, SUM = \frac{1}{b-a}\int_{a}^{b}dx\\or, SUM = \frac{1}{b-a}[x]_{a}^{b}\\or, SUM = \frac{1}{b-a}(b-a)\\or, SUM = 1[/tex]
The sum can also be found using the graph attached, calculating the area of the red rectangle.
∴ The sum of the probabilities in a uniform probability distribution is 1.
Hence, option C is the right choice.
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