Question

6. Students in one statistics course need to earn a grade of at least C, otherwise they need to repeat the course. It is also known that 85% of all students who attend class regularly will earn a grade of at least C, while only 30% of those students who do not attend class regularly will earn a grade of at least C. Historically, 80% of all students in this course attend class regularly. You must explicitly define any events you use and justify any computations through the use of a formula.

(a) If a student is randomly selected, what is the probability that they will achieve a grade of at least C?

(b) A randomly selected student earned a grade of at least C. What is the probability that this student attended class regularly?

Answer 1

We have two events:

i) Getting a grade of C

ii) Regularly attending the classes

First, we need to make the distribution table:

	Attends class regularly	Do not attend class regularly	Sum
Grade at least C	85% of 0.80 = 0.68	30% of 0.20 = 0.06	0.74
Grade less than C	0.80 - 0.68 = 0.12	0.20 - 0.06 = 0.14	0.26
Sum	0.80	0.20	1

a) Th probability that they will achieve a grade of at least C is = 0.74

b) The probability that a student attends class regularly given that the student earned a grade of at least C is

= 0.68/0.74

= 0.9189

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