Answered: Consider two events with P(A)=.4,…

Consider two events with P(A)=.4, P(B|A)=.5 and P(A or B)=.7 a) find P(A and B)= b) find P(B)= c) Are A and B independent? Explain d) Find P(A|B)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Consider two events with P(A)=.4, P(B|A)=.5 and P(A or B)=.7

a) find P(A and B)=

b) find P(B)=

c) Are A and B independent? Explain

d) Find P(A|B)

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Expert Solution

Step 1

The provided information are:

$P (A) = 0.4 P (B | A) = 0.5 P (A o r B) = 0.7$

by using the following formulas calculate the given probability :

$P (B | A) = \frac{P (A a n d B)}{P (A)} a n d P (A o r B) = P (A) + P (B) - P (A a n d B)$

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