Question

How to slove problems e to j ?

1. A statistics class for engineers consists of 53 students. The students in the class are classified based on their college major and sex as shown in the following contingency table:

	College Major
Sex	Industrial Engineering	Mechanical Engineering	Electrical Engineering	Civil Engineering	Total
Male	15	6	7	2	30
Female	10	4	3	6	23
Total	25	10	10	8	53

If a student is selected at random from the class by the instructor to answer a question, find the following probabilities. Report your answer to 4 decimal places.

Consider the following events:

A: The selected student is a female.

B: The selected student is mechanical engineering major.

C: The selected student is civil engineering major.

D: The selected student is industrial engineering major.

Note: Indicate the type of probability as marginal, joint or conditional when asked.

a) Find the probability that the randomly selected student is a female. Indicate the type of probability.

P(Female) = 23 / 53 = 0.4340

Marginal probability

b) Find the probability that the randomly selected student is mechanical engineering major. Indicate the type of probability.

P(Mechanical Engineer) = 10 / 53 = 0.1887

Marginal probability

c)   Find the probability that the randomly selected student is female mechanical engineering major. Indicate the type of probability.

P(Female Mechanical ) = 4/ 53 = 0.0755

Joint probability

d) Given that the selected student is mechanical engineering major, what is the probability that the student is female? Indicate the type of probability.

P(Female Mechanical) = 4 / 10 =0.4

Conditional probability.

e)   Based on your answers on part a and d, are sex and college major of students in this class independent? Provide a mathematical argument?

  

f)   Consider the events A and B. Are sex and college major mutually exclusive events? Provide a mathematical argument to justify your answer.

g)    Find the probability that the randomly selected student is female or mechanical engineering college major.

h) Consider the events C and D. Are college major mutually exclusive events? Provide a mathematical argument to justify your answer.

i)   Find the probability that the randomly selected student is civil or industrial engineering college major.

j) What is the probability that a randomly selected student is neither a female nor a mechanical engineering college major?

Answer 1

e) For Independent event X and Y

P(X|Y) = P(X)

Here ,

Hence sex and college major of students in this class are not independent.

f) P(A) = 0.4340

P(B) = 0.1887

For Mutually Exclusive Events X and Y

Here ,

Hence the events A and B are not mutually exclusive.

g)

h)

Considering the events C and D, yes they are mutually exclusive because the student can select only one college major . There is no students who can select civil engineering major and industrial engineering major. Hence they are mutually exclusive

i)

j)

The probability that a randomly selected student is neither a female nor a mechanical engineering college major is