Question

An instructor who taught two sections of engineering statistics last term, the first with 20 students and the second with 35, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 16 graded projects.

(a) What is the probability that exactly 10 of these are from the second section? (Round your answer to four decimal places.)


(b) What is the probability that exactly 6 of these are from the first section? (Round your answer to four decimal places.)


(c) What is the probability that at all 16 of these are from the same section? (Round your answer to six decimal places.)

Answer 1

Strength of students in 1st section = 20

Strength of students in 2nd section = 35

We opt-out 16 graded projects out of 20+35 = 55 projects.

a.

The probability that exactly 10 of these are from the second section (i.e 10 from 2nd section and 6 from 1st seciion)

= = (183579396 * 38760) / 29749251314475 = 0.2391837

b.

The probability that exactly 6 of these are from the first section (i.e 6 from 1st section and remaining 10 from 2nd section )

= = (38760* 183579396 ) / 29749251314475 = 0.2391837

c.

The probability that at all 16 of these are from the same section i.e (16 from 1st section or 16 from 2nd section)

= + = (4845 + 4059928950) / 29749251314475 = 0.000136471