Question

In: Statistics and Probability

During the recent graduation season in Namibia a total of 8000 students graduated from three different...

During the recent graduation season in Namibia a total of 8000 students graduated from three different universities UNAM, NUST and IUM. Of the 8000 graduates, 4000 students graduated from UNAM, 3000 students graduated from NUST, while the rest of the students graduated from IUM. A total of 85 out of every 100 students from UNAM graduated from their Business School, while at NUST, 65 out of every 100 students graduated from their Business School, and at IUM, 60 out of every 100 students graduated from their Business School. The Minister of Education in Namibia, randomly selects a student who graduated during this graduation season:

1.1) Find the probability that the selected graduate is from a Business School. (7)

1.2) Calculate the probability that the randomly selected graduate from a Business School is from NUST. (5)

Expert Solution

1.1) We are asked to calculate the probability that the selected graduate is from a Business school.

Probability of UNAM's Business school as the selected Business school=(since there are three Business schools, probability of selecting one out of three schools is 1/3)denoted by A

Probability that the graduate is from UNAM= denoted by B

Probability of NUST's Business school is the selected Business school= denoted by C

Probability that the graduate is from NUST= denoted by D.

Probability of IUM's business school is the selected Business school= denoted by E.

Probability that the graduate is from IUM= denoted by F.

So, probability that the selected graduate is from a Business school denoted by G is,

(taking 3 and 100 common in the denominator)

Hence the probability that the selected graduate is from a Business school is 0.7

1.2) We are asked to calculate the probability that the randomly selected graduate from a Business school is from NUST.

Let A be the event that NUST's Business school is selected.

Probability of NUST's Business school is selected, (since there are three Business schools, probability of one of the Business school is selected is 1/3).

Let B be the event that the graduate is from NUST's Business school.

Probability that the graduate is from NUST's Business school is,

Let the event that the randomly selected graduate from a Business school is from NUST be denoted by C.

Probability that the randomly selected graduate from a Business school is from NUST,

Hence the probability that the randomly selected graduate from a Business school is from NUST is 0.217

orchestra answered 2 years ago

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