Questions: The sum of all the probabilities in a discrete probability distribution must be equal to 1

The sum of all the probabilities in a discrete probability distribution must be equal to 1
Transcript text: Part 2 of 2 The sum of all the probabilities in a discrete probability distribution must be equal to $\square$
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Solution

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Solution Steps

To solve this problem, we need to understand that in a discrete probability distribution, the sum of all individual probabilities must equal 1. This is a fundamental property of probability distributions.

Step 1: Define the Probabilities

We are given a discrete probability distribution with the following probabilities: \[ P_1 = 0.2, \quad P_2 = 0.3, \quad P_3 = 0.1, \quad P_4 = 0.4 \]

Step 2: Calculate the Sum of Probabilities

We calculate the sum of all probabilities: \[ \text{Sum} = P_1 + P_2 + P_3 + P_4 = 0.2 + 0.3 + 0.1 + 0.4 = 1.0 \]

Step 3: Validate the Probability Distribution

According to the properties of probability distributions, the sum of all probabilities must equal \(1\): \[ \text{Sum} = 1.0 \] Since the calculated sum is equal to \(1\), the distribution is valid.

Final Answer

The sum of all the probabilities in a discrete probability distribution must be \( \boxed{1} \).

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