Determining a Missing Probability In Exercises 25 and 26, determine the missing probability for the probability distribution.

Verified step by step guidance

1. Step 1: Recall that for a probability distribution, the sum of all probabilities must equal 1. This is a fundamental property of probability distributions.
2. Step 2: Write the equation for the sum of probabilities: P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1.
3. Step 3: Substitute the known probabilities into the equation: 0.05 + P(1) + 0.23 + 0.21 + 0.17 + 0.11 + 0.08 = 1.
4. Step 4: Combine all the known probabilities: 0.05 + 0.23 + 0.21 + 0.17 + 0.11 + 0.08 = 0.85.
5. Step 5: Solve for the missing probability P(1) by subtracting the sum of the known probabilities from 1: P(1) = 1 - 0.85.

Key Concepts

Probability Distribution

A probability distribution describes how the probabilities are distributed over the values of a random variable. It provides a complete description of the likelihood of each possible outcome. In this case, the distribution is discrete, as it lists specific values of x and their corresponding probabilities.

Sum of Probabilities

In any probability distribution, the sum of all probabilities must equal 1. This principle is fundamental in determining missing probabilities, as it allows us to calculate the unknown value by subtracting the sum of known probabilities from 1. This ensures that the distribution is valid and adheres to the rules of probability.

Missing Probability Calculation

To find a missing probability in a distribution, you can use the equation derived from the sum of probabilities. By adding the known probabilities and subtracting this sum from 1, you can isolate and determine the unknown probability. This method is essential for completing the probability distribution accurately.