Question

In: Statistics and Probability

A statistics class for engineers consists of 53 students. The students in the class are classified...

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. (total 80 points)

Consider the following events:

A: The selected student is a male.

B: The selected student is industrial engineering major.

C: The selected student is civil engineering major.

D: The selected student is electrical engineering major.

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

Find the probability that the randomly selected student is a male. Indicate the type of probability. (8 + 2 = 10 points)

Find the probability that the randomly selected student is industrial engineering major. Indicate the type of probability. (8 + 2 = 10 points)

Find the probability that the randomly selected student is male industrial engineering major. Indicate the type of probability. (8 + 2 = 10 points)

Given that the selected student is industrial engineering major, what is the probability that the student is male? Indicate the type of probability.

(8 + 2 = 10 points)

Based on your answers on part a and d, are sex and college major of students in this class independent? Provide a mathematical argument? (6 points)

Consider the events A and B. Are sex and college major mutually exclusive events? Provide a mathematical argument to justify your answer. (6 points)

Find the probability that the randomly selected student is male or industrial engineering college major. (10 points)

Consider the events C and D. Are college major mutually exclusive events? Provide a mathematical argument to justify your answer. (6 points)

Find the probability that the randomly selected student is civil or electrical engineering college major. (6 points)

What is the probability that a randomly selected student is neither a male nor an industrial engineering college major? (6 points)

Expert Solution

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Thank you.

orchestra answered 3 years ago

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