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The tree diagram represents an experiment consisting of two trials. Enter the probability to the hundredths place. Do not round. .3 C P(D) = [?] Enter

The tree diagram represents an experiment consisting of two trials. Enter the probability to the hundredths place. Do not round. .3 C P(D) = [?] Enter

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Understanding Probability with Tree Diagrams Tree diagrams are particularly useful in probability theory for visualizing and calculating the probabilities of various outcomes of an experiment, particularly when there are multiple stages or events. Let's analyze a given tree diagram to solve for a specific probability. #### Problem Statement The tree diagram represents an experiment consisting of two trials. Following the diagram, we need to calculate the probability \( P(D) \). Enter the probability to the hundredths place. Do not round. #### Tree Diagram Breakdown The provided tree diagram is structured as follows: 1. **First Trial:** - Event A has two possible outcomes: - Outcome C with a probability of 0.3 - Outcome D with a probability of 0.7 - Event B has two possible outcomes: - Outcome C with a probability of 0.2 - Outcome D with a probability of 0.8 2. **Second Trial:** - Outcome A leads to: - A sub-outcome C with a probability of 0.3 - A sub-outcome D with a probability of 0.7 - Outcome B leads to: - A sub-outcome C with a probability of 0.2 - A sub-outcome D with a probability of 0.8 We aim to find the overall probability of the event D occurring (\(P(D)\)). #### Calculating the Probability \(P(D)\) 1. **Paths leading to D:** - Path 1: A followed by D - Probability = \( P(A) \times P(D|A) = 0.6 \times 0.7 = 0.42 \) - Path 2: B followed by D - Probability = \( P(B) \times P(D|B) = 0.4 \times 0.8 = 0.32 \) 2. **Total probability of D (Combining paths leading to D):** - Total \( P(D) = 0.42 + 0.32 = 0.74 \) #### Final Answer \[ P(D) = 0.74 \] Please enter the probability \( P(D) \) in the box provided as 0.74.
Transcribed Image Text:### Understanding Probability with Tree Diagrams Tree diagrams are particularly useful in probability theory for visualizing and calculating the probabilities of various outcomes of an experiment, particularly when there are multiple stages or events. Let's analyze a given tree diagram to solve for a specific probability. #### Problem Statement The tree diagram represents an experiment consisting of two trials. Following the diagram, we need to calculate the probability \( P(D) \). Enter the probability to the hundredths place. Do not round. #### Tree Diagram Breakdown The provided tree diagram is structured as follows: 1. **First Trial:** - Event A has two possible outcomes: - Outcome C with a probability of 0.3 - Outcome D with a probability of 0.7 - Event B has two possible outcomes: - Outcome C with a probability of 0.2 - Outcome D with a probability of 0.8 2. **Second Trial:** - Outcome A leads to: - A sub-outcome C with a probability of 0.3 - A sub-outcome D with a probability of 0.7 - Outcome B leads to: - A sub-outcome C with a probability of 0.2 - A sub-outcome D with a probability of 0.8 We aim to find the overall probability of the event D occurring (\(P(D)\)). #### Calculating the Probability \(P(D)\) 1. **Paths leading to D:** - Path 1: A followed by D - Probability = \( P(A) \times P(D|A) = 0.6 \times 0.7 = 0.42 \) - Path 2: B followed by D - Probability = \( P(B) \times P(D|B) = 0.4 \times 0.8 = 0.32 \) 2. **Total probability of D (Combining paths leading to D):** - Total \( P(D) = 0.42 + 0.32 = 0.74 \) #### Final Answer \[ P(D) = 0.74 \] Please enter the probability \( P(D) \) in the box provided as 0.74.
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