In probability theory, a discrete distribution consists of a finite or countably infinite number of values, each with an associated probability. For a given discrete probability distribution, the sum of all the probabilities must equal 1. If we have a situation where one of the probabilities is missing, we can determine its value by ensuring that the total probability sums to 1.
Let’s say we have a discrete distribution with the following probabilities:
- P(A) = 0.2
- P(B) = 0.3
- P(C) = x (missing probability)
- P(D) = 0.5
To find the missing probability (x), we simply set up the equation:
P(A) + P(B) + P(C) + P(D) = 1
Substituting the known values, we get:
0.2 + 0.3 + x + 0.5 = 1
Combining the known probabilities, we find:
1 + x = 1
This leads us to:
x = 1 – 1
x = 0
Thus, the value of the missing probability is 0. This means that for the given distribution to represent a valid discrete distribution, the fourth event must not occur, ensuring all probability values sum up to 1.