https://file.aiquickdraw.com/mathbot/file/1729034608094mqnj9ksu.jpg

The table shows the probability distribution for a discrete random variable \( x \), where each \( P(x) \) represents the probability associated with each possible value of \( x \). The sum of all probabilities in a probability distribution must equal 1.

From the table:

\[
P(0) + P(1) + P(2) + P(3) = 1
\]

We know:

\[
P(1) = 0.25, \quad P(2) = 0.20, \quad P(3) = 0.45
\]

Let \( P(0) = ? \). So, the equation becomes:

\[
P(0) + 0.25 + 0.20 + 0.45 = 1
\]

Now, summing the known probabilities:

\[
0.25 + 0.20 + 0.45 = 0.90
\]

Thus,

\[
P(0) + 0.90 = 1
\]

\[
P(0) = 1 - 0.90 = 0.10
\]

So, the missing probability \( P(0) \) is 0.10.

Would you like more details or have any questions about this? 

Here are 5 related questions:
1. What is a probability distribution?
2. How do you verify that a set of probabilities is valid?
3. What are the properties of a discrete probability distribution?
4. How would this change for a continuous distribution?
5. Can probabilities be negative?

**Tip**: Always ensure that the sum of all probabilities in any probability distribution equals 1.

Determine the value of the missing probability for the random variable x where P(x) represents the probability. Given probabilities: P(1) = 0.25, P(2) = 0.2, P(3) = 0.45.

Learn how to find the missing probability in a discrete random variable probability distribution. Given: P(1) = 0.25, P(2) = 0.2, P(3) = 0.45. Understand how to ensure that the sum of probabilities equals 1, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation