Last semester, I taught two sections of a same class; Section A with 20 students and Section B with 30. Before grading their final exams, I randomly mixed all the exams I together. I graded 12 exams at the first sitting. (i) Of those 12 exams, the probability that exactly 5 of these are from the Section B is (You do not need to simplify your answers.) . (ii) Of those 12 exams, the probability that they are not all from the same section is (You do not need to simplify your answers.)

Answers

Answer 1

1. The probability is approximately 0.1823.

2. The probability that the 12 exams are not all from the same section is 0.6756

How to calculate the probability

1. The probability that exactly 5 of the 12 exams are from Section B is:

P(X = 5) = (12 choose 5) * 0.6 × 0.6⁴ * (1 - 0.6)⁷

= 0.1823

2.  The probability that all 12 exams are from the same section is:

P(all from A) + P(all from B) = (20/50)¹² + (30/50)¹²

≈ 0.0132 + 0.3112

≈ 0.3244

Therefore, the probability that the 12 exams are not all from the same section is:

P(not all from same section) = 1 - P(all from same section)

≈ 1 - 0.3244

≈ 0.6756

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