Math Problem Statement

Complete the following probability distribution table:

Probability Distribution Table X P(X) -14 0.5 8 0.1 18 0.1 80 X

Solution

To complete the probability distribution table, remember that the sum of all probabilities P(X)P(X) in a probability distribution must equal 1.

Given:

P(14)=0.5,P(8)=0.1,P(18)=0.1,P(80)=XP(-14) = 0.5, \, P(8) = 0.1, \, P(18) = 0.1, \, P(80) = X

The equation becomes: 0.5+0.1+0.1+X=10.5 + 0.1 + 0.1 + X = 1

Solve for XX:

X=1(0.5+0.1+0.1)=10.7=0.3X = 1 - (0.5 + 0.1 + 0.1) = 1 - 0.7 = 0.3

Completed Probability Distribution Table:

XXP(X)P(X)
-140.5
80.1
180.1
800.3

The missing probability is P(80)=0.3P(80) = 0.3.


Would you like additional examples or detailed explanations?

5 Related Questions:

  1. How can you verify if a given probability distribution table is valid?
  2. What is the importance of the sum of probabilities equaling 1?
  3. How do you find the expected value of a probability distribution?
  4. What happens if the probabilities in a distribution sum to more or less than 1?
  5. Can you construct a probability distribution for a continuous variable?

Tip:

For discrete probability distributions, always double-check that all probabilities are non-negative and their total equals exactly 1.

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Math Problem Analysis

Mathematical Concepts

Probability
Probability Distribution
Basic Algebra

Formulas

Sum of probabilities in a distribution: ∑P(X) = 1

Theorems

Fundamental Rule of Probability Distributions

Suitable Grade Level

Grades 9-10