Math Problem Statement
Given the probability distribution table with missing values for X = 2 and X = 6, find the missing probabilities assuming the total probability must sum to 1.
Solution
It seems you've uploaded an image showing part of a probability distribution table with some missing probabilities. Let’s analyze the table:
\hline \text{Value } x \text{ of } X & P(X = x) \\ \hline 2 & ? \\ 3 & 0.20 \\ 4 & 0.20 \\ 5 & 0.15 \\ 6 & ? \\ \hline \end{array}$$ ### Step 1: Sum of all probabilities In a valid probability distribution, the sum of all probabilities must equal 1: $$P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 1$$ ### Step 2: Known values From the table, we already know: $$P(X = 3) = 0.20, \quad P(X = 4) = 0.20, \quad P(X = 5) = 0.15$$ Thus, the sum of known probabilities is: $$0.20 + 0.20 + 0.15 = 0.55$$ ### Step 3: Find the missing probabilities Let the missing probabilities be $$P(X = 2) = p_1$$ and $$P(X = 6) = p_2$$. Then: $$p_1 + p_2 + 0.55 = 1$$ This simplifies to: $$p_1 + p_2 = 0.45$$ Thus, the missing probabilities must sum to 0.45. However, without additional information, they could be any two numbers that satisfy this equation. Would you like to assign equal probabilities to $$P(X = 2)$$ and $$P(X = 6)$$, or is there another assumption you'd prefer? Let me know! --- Do you have any questions or need further clarifications? Here are some follow-up questions: 1. How do we check if a probability distribution is valid? 2. What is the significance of the sum of probabilities in a distribution? 3. Could you apply this to solve a related problem, like finding expected value? 4. How would you compute variance from this distribution? 5. Why is it important for probabilities to sum to 1? **Tip:** The sum of all probabilities in a distribution must always equal 1.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Probability Distribution
Formulas
Sum of probabilities must equal 1
p1 + p2 + 0.55 = 1
Theorems
Total Probability Theorem
Suitable Grade Level
Grades 9-12
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