### Activity: Supply the Missing Quantities#### Diagram DescriptionThe diagram is a probability tree with two main branches:1. **Branch A**: - Probability to reach node A is 0.7. - From node A, two branches emerge: - **To C** with a probability of 0.2. - **To D** (probability not provided).2. **Branch B**: - Probability to reach node B is 0.3 (implied as the complement of 0.7). - From node B, two branches emerge: - **To C** (probability not provided). - **To D** with a probability of 0.8.#### OutcomeFill in the probabilities for the outcomes:\[ P(A \cap C) = \]\[ P(A \cap D) = \]\[ P(B \cap C) = \]\[ P(B \cap D) = \]Use the information given in the diagram to calculate the missing probabilities based on the structure of the tree.

Total probability is 1. Using that we get:

Answered: Supply the missing quantities. Figure…

Math

Probability

Supply the missing quantities. Figure Description 0.2 0.7 D B 0.8 (D Outcome P(A n C) = P(A n D) P(B n C) = P(B n D) =

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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### Activity: Supply the Missing Quantities

#### Diagram Description

The diagram is a probability tree with two main branches:

1. **Branch A**:
- Probability to reach node A is 0.7.
- From node A, two branches emerge:
- **To C** with a probability of 0.2.
- **To D** (probability not provided).

2. **Branch B**:
- Probability to reach node B is 0.3 (implied as the complement of 0.7).
- From node B, two branches emerge:
- **To C** (probability not provided).
- **To D** with a probability of 0.8.

#### Outcome

Fill in the probabilities for the outcomes:

\[ P(A \cap C) = \]
\[ P(A \cap D) = \]
\[ P(B \cap C) = \]
\[ P(B \cap D) = \]

Use the information given in the diagram to calculate the missing probabilities based on the structure of the tree.

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