# Finite Element Methods Probabilities using Venn diagram

Conditional Probabilities

The records of Midwestern University show that in one semester, 38% of the students failed mathematics, 27% of the students failed Physics and 9% of the students failed mathematics and Physics. A student is selected at random.

(a)If a student failed Physics, what is the probability that he or she failed

mathematics?

(b)If a student failed Mathematics, what is the probability that he or she failed

Physics?

(c)What is the probability that he or she fails Mathematics or Physics?

(d)Find the probability that he or she failed in none of the two subjects.

Please see the attachment for the full description of the question.

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Solution:

(Note : Please see the attachment for full step by step solution. Below are given just a few lines from the solution)

Let M denote the event that the student has failed in ...

#### Solution Summary

The solution in the attached file is given with step by step explanation using standard notations so that the student could solve other problems of this type independently by himself to prepare for tests/examinations.

The solution is given in MS word document and is in its original content and does not contain any links to other material.

The solution is supplemented with Venn diagram, making the concept clear how to draw a venn diagram in such problems and how to represent the probabilites in Venn Diagram.