How would you find the probability of this equation? You are given that Pr (A) = 2, Pr (AUB) = , Pr (B|A) = 1, Pr (C|B) = ,andPr (C|An B) = 1/1.Find Pr (A|BC).

Given information: PrA=25..........(1)PrA∪B=35.............(2)PrB|A=14PrA∩BPA=14PrA∩B=14*PA…

Answered: How would you find the probability of…

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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Question

How would you find the probability of this equation?

You are given that Pr (A) = 2, Pr (AUB) = , Pr (B|A) = 1, Pr (C|B) = ,and
Pr (C|An B) = 1/1.
Find Pr (A|BC).

Expert Solution

Step 1

Given information:

$P r (A) = \frac{2}{5} . . . . . . . . . . (1) P r (A \cup B) = \frac{3}{5} . . . . . . . . . . . . . (2) P r (B | A) = \frac{1}{4} \frac{P r (A \cap B)}{P (A)} = \frac{1}{4} P r (A \cap B) = \frac{1}{4} * P (A) = \frac{1}{4} * \frac{2}{5} = \frac{1}{10} . . . . . . . . . . . . . . (3)$

By using the equations (1), (2) and (3),

$P (A \cup B) = P (A) + P (B) - P (A \cap B) \frac{3}{5} = \frac{2}{5} + P (B) - \frac{1}{10} \frac{3}{5} = P (B) + \frac{3}{10} P (B) = \frac{3}{5} - \frac{3}{10} = \frac{3}{10}$

$P r (C | B) = \frac{1}{3} \frac{P r (B \cap C)}{P (B)} = \frac{1}{3} P r (B \cap C) = \frac{1}{3} * P (B) = \frac{1}{3} * \frac{3}{10} = \frac{1}{10}$

$P r (C | A \cap B) = \frac{1}{2} \frac{P r (A \cap B \cap C)}{P r (A \cap B)} = \frac{1}{2} P r (A \cap B \cap C) = \frac{1}{2} * P r (A \cap B) = \frac{1}{2} * \frac{1}{10} = \frac{1}{20}$