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Compute the indicated quantity. P(A | B) = 0.3, P(B) = 0.6. Find P(A N B). %3D P(A N B) = %3D

Compute the indicated quantity. P(A | B) = 0.3, P(B) = 0.6. Find P(A N B). %3D P(A N B) = %3D

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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--- **Problem Statement:** Compute the indicated quantity. Given: - \( P(A \mid B) = 0.3 \) - \( P(B) = 0.6 \) Find \( P(A \cap B) \). **Solution:** The probability \( P(A \cap B) \) can be calculated using the formula for conditional probability: \[ P(A \cap B) = P(A \mid B) \times P(B) \] Substitute the given values: \[ P(A \cap B) = 0.3 \times 0.6 = 0.18 \] \[ P(A \cap B) = \boxed{0.18} \] ---
Transcribed Image Text:--- **Problem Statement:** Compute the indicated quantity. Given: - \( P(A \mid B) = 0.3 \) - \( P(B) = 0.6 \) Find \( P(A \cap B) \). **Solution:** The probability \( P(A \cap B) \) can be calculated using the formula for conditional probability: \[ P(A \cap B) = P(A \mid B) \times P(B) \] Substitute the given values: \[ P(A \cap B) = 0.3 \times 0.6 = 0.18 \] \[ P(A \cap B) = \boxed{0.18} \] ---
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