Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogousevent for a MasterCard where P(A) = 0.50, P(B) = 0.35, and P(A N B) = 0.30. Calculate and interpret each of the following probabilities (a Venn diagram might help).(Round your answers to four decimal places.)(a)P(B | A)(b) P(B' | A)(c) P(A | B)

Answered: event for a MasterCard where P(A) =…

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 randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous
event for a MasterCard where P(A) = 0.50, P(B) = 0.35, and P(A N B) = 0.30. Calculate and interpret each of the following probabilities (a Venn diagram might help).
(Round your answers to four decimal places.)
(a)
P(B | A)
(b) P(B' | A)
(c) P(A | B)

Expert Solution

Step 1

Conditional probability is the probability of happening of any event given that an another event has already occurred prior to it. Let there are two events, event A and event B then, the conditional probability of event A given that event B has already occurred is given by:

$P (A | B) = \frac{P (A \cap B)}{P (B)}$

Let there is an event A and its probability of occurrence is P(A). The non happening of the event A is denoted as A', called as complement of event A, given as $P (A') = 1 - P (A)$ .