This image illustrates a probability tree diagram for drawing balls from a bag. The bag contains two types of balls: Blue (B) and Yellow (Y). Specifically, there are 3 Blue balls and 5 Yellow balls, as indicated at the start of the diagram. ### Breakdown of the Diagram: 1. First Branch: - The first decision point splits into two branches for the first draw: - Blue (3/8): The probability of drawing a Blue ball first is 3 out of 8. - Yellow (5/8): The probability of drawing a Yellow ball first is 5 out of 8. 2. Second Branch (after drawing a Blue ball first): - If a Blue ball is drawn first (probability 3/8), there are two subsequent branches: - Blue (2/7): The probability of drawing another Blue ball is 2 out of 7, since one Blue ball has already been removed. - Yellow (5/7): The probability of drawing a Yellow ball is 5 out of 7. 3. Second Branch (after drawing a Yellow ball first): - If a Yellow ball is drawn first (probability 5/8), there are two subsequent branches: - Blue (3/7): The probability of drawing a Blue ball is 3 out of 7. - Yellow (4/7): The probability of drawing another Yellow ball is 4 out of 7, since one Yellow ball has already been removed. ### Summary: The diagram effectively demonstrates how probabilities change based on the sequence of events, specifically the effect of removing a ball from the bag on the probabilities of subsequent draws. Each branch corresponds to a potential outcome and its associated probability, helping visualize the concepts of probability in sequential actions.

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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Related questions

Question

Suppose 3 blue and 5 yellow identical objects are in a jar. A blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. The following tree diagram depicts all the possible random outcomes and their probabilities.

Note: Please enter your answers below in fraction form.

a) What is the conditional probability P (Yellow | Yellow)

b) What is the probability of obtaining a final outcome with first a yellow object and then a blue object?

This image illustrates a probability tree diagram for drawing balls from a bag. The bag contains two types of balls: Blue (B) and Yellow (Y). Specifically, there are 3 Blue balls and 5 Yellow balls, as indicated at the start of the diagram.

### Breakdown of the Diagram:

1. **First Branch:**
- The first decision point splits into two branches for the first draw:
- **Blue (3/8):** The probability of drawing a Blue ball first is 3 out of 8.
- **Yellow (5/8):** The probability of drawing a Yellow ball first is 5 out of 8.

2. **Second Branch (after drawing a Blue ball first):**
- If a Blue ball is drawn first (probability 3/8), there are two subsequent branches:
- **Blue (2/7):** The probability of drawing another Blue ball is 2 out of 7, since one Blue ball has already been removed.
- **Yellow (5/7):** The probability of drawing a Yellow ball is 5 out of 7.

3. **Second Branch (after drawing a Yellow ball first):**
- If a Yellow ball is drawn first (probability 5/8), there are two subsequent branches:
- **Blue (3/7):** The probability of drawing a Blue ball is 3 out of 7.
- **Yellow (4/7):** The probability of drawing another Yellow ball is 4 out of 7, since one Yellow ball has already been removed.

### Summary:

The diagram effectively demonstrates how probabilities change based on the sequence of events, specifically the effect of removing a ball from the bag on the probabilities of subsequent draws. Each branch corresponds to a potential outcome and its associated probability, helping visualize the concepts of probability in sequential actions.

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