Suppose that a class consists of 20 students. The table gives a breakdown of the

Question

Suppose that a class consists of 20 students. The table gives a breakdown of the students by year and major. i. If a student is randomly selected, find the probability that the student is a junior ii. If a student is randomly selected, find the probability that the student is a junior. iii. If a student is randomly selected, find the probability that the student is an engineering major. iv. Given that a randomly selected student is a junior, find the probability that the student is a engineering major. (b) Are the events "student is a junior" and "student is an engineering major" independent? Justify your answer. A group of 3 students is randomly selected. Find the probability that the group includes one computer science major, one engineering major, and one mathematics major.

Explanation / Answer

iv) P( enginer |Given junior) =4 /10 = .4

This is right , I don't know why your assignement corrector has market it wrong

b)
Here they asked you to prove mathematically.

When two events are said to be independent of each other, what this means is that the probability that one event occurs in no way affects the probability of the other event occurring

So, since there is a intercept of 4 people who are engineer and are junior, they are not mutually exclusice and hence changing one can change the other.

So, they aren't indepdent events

c)

Any 3 can be selected in 20C3 ways out of total 20 people
1 comp. science , 1 engg, 1 math can be choosen in 5C1*9C1*6C1 = 270 ways
So, P = 270/20C3 = .237

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