According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30% and 20% If a randomly selected student lives in the dormitory, what is the probability that the student is a freshman (tip: Bayes theorem)? a. 0.331 b 0.439 c. 0.638 : d. 0.532

The probability that the student is a freshman is 52.32% If a randomly selected student lives in the dormitory. The right answer is d.

Explanation:

According to the data we have the following:

p(freshman) = 0.35

p(sophomore) = 0.25

p(Junior) = 0.16

p(senior) = 0.24

Also:

p(Dormitory/freshman) = 0.8

p(Dormitory/sophomore) = 0.6

p(Dormitory/Junior) = 0.3

p(Dormitory/Senior) = 0.2

Therefore, to calculate the probability that the student is a freshman If a randomly selected student lives in the dormitory we would habe to use the

Bayes theorem

Hence, p(Freshman/Dormitory) = p(Dormitory/freshman) * p(freshman) / {p(Dormitory/freshman) * p(freshman) +  p(Dormitory/sophomore) * p(sophomore) + p(Dormitory/Junior) * p(Junior) +   p(Dormitory/Senior) * p(senior)}

= 0.8 * 0.35 / { 0.8*0.35 + 0.6*0.25 + 0.3*0.16 + 0.2 * 0.24}

= 0.28/0.526

= 0.532. The probability that the student is a freshman is 52.32%

2 weeks ago lol enoy your dunce cap

it's actually a very difficult task, due to not many people can make 2 million dollars in 2 years. besides that, to the not-so-realistic ideas, you can create a business. it could be practically anything, but make it into a business that isn't that known yet, you get me? also, lets not forget about stock market. that's where all the good stuff happens. use investments at the beginning and begin to raise up your business or whatever you're going to do. as this is a very non-realistic idea, it's still worth the shot!