The tree diagram represents an experiment consisting of two trials. .5 P(A and D) = [ ? ] Enter 6. 3.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 59E
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please if somebody can help me find the answer to p(A and D)=

**Multiple Events: Probability and Statistics**

The tree diagram represents an experiment consisting of two trials.

(Tree Diagram Description)
- The diagram starts with an initial node, branching into two paths labeled \( A \) and \( B \), each with probabilities \( 0.5 \).

  - From node \( A \), there are two further branches leading to outcomes \( C \) and \( D \):
    - \( A \rightarrow C \) with a probability of \( 0.4 \).
    - \( A \rightarrow D \) with a probability of \( 0.6 \).

  - From node \( B \), there are also two branches leading to outcomes \( C \) and \( D \):
    - \( B \rightarrow C \) with a probability of \( 0.3 \).
    - \( B \rightarrow D \) with a probability of \( 0.7 \).

**Problem Statement:**
\[ P(A \text{ and } D) = [?] \]

(Answer Input Box)
\[ \text{Enter} \]

**Copyright © 2003 - 2020 Acellus Corporation. All Rights Reserved.**

This problem requires calculating the joint probability of events \( A \) and \( D \). To solve it, multiply the probability of \( A \) by the probability of \( D \) given \( A \):

\[ P(A \text{ and } D) = P(A) \times P(D|A) \]
\[ P(A) = 0.5 \]
\[ P(D|A) = 0.6 \]
\[ P(A \text{ and } D) = 0.5 \times 0.6 = 0.3 \]
Transcribed Image Text:**Multiple Events: Probability and Statistics** The tree diagram represents an experiment consisting of two trials. (Tree Diagram Description) - The diagram starts with an initial node, branching into two paths labeled \( A \) and \( B \), each with probabilities \( 0.5 \). - From node \( A \), there are two further branches leading to outcomes \( C \) and \( D \): - \( A \rightarrow C \) with a probability of \( 0.4 \). - \( A \rightarrow D \) with a probability of \( 0.6 \). - From node \( B \), there are also two branches leading to outcomes \( C \) and \( D \): - \( B \rightarrow C \) with a probability of \( 0.3 \). - \( B \rightarrow D \) with a probability of \( 0.7 \). **Problem Statement:** \[ P(A \text{ and } D) = [?] \] (Answer Input Box) \[ \text{Enter} \] **Copyright © 2003 - 2020 Acellus Corporation. All Rights Reserved.** This problem requires calculating the joint probability of events \( A \) and \( D \). To solve it, multiply the probability of \( A \) by the probability of \( D \) given \( A \): \[ P(A \text{ and } D) = P(A) \times P(D|A) \] \[ P(A) = 0.5 \] \[ P(D|A) = 0.6 \] \[ P(A \text{ and } D) = 0.5 \times 0.6 = 0.3 \]
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