1. A statistics class for engineers consists of 53 students. The students in the
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Question
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.
b) Find the probability that the randomly selected student is mechanical engineering major. Indicate the type of probability.
c) Find the probability that the randomly selected student is female mechanical engineering major. Indicate the type of 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.
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?
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
Explanation / Answer
A)
P(Female) = 23C1 / 53C1 = 23 / 53 = 0.4340
B)
P(Mechanical Engineer) = 10/53 = 0.1887
C)
P(Civil Engineer) = 8/53 = 0.1509
D)
P(industrial engineer) = 25/53 = 0.4717
a)
P(Female) = 23C1 / 53C1 = 23 / 53 = 0.4340
Marginal probability
b)
P(Mechanical Engineer) = 10/53 = 0.1887
Marginal probability
c)
Joint probability
P(Female and mechanical engineer) = 4/53 = 0.0755
d)
P(F|mechanical) = 4/10 = 0.4
Conditional probability
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