Question

Data 105, 91, 52, 86, 100, 96, 98, 109, 96, 88,70

Suppose we have assigned grades for the 11 students in our data:Grade A for students who scored ≥ 90; B for students who scored ≥ 80 and < 90; C for students who scored ≥ 70 and < 80; D for students who scored ≥ 60 and < 70; F for students who scored < 60.

Following the above grade scheme, we observe that we have 7 students who received grade A, 1 student received grade B, 0 students received grade C, 0 students received grade D and 1 student received grade F.

Using this, please answer the following questions:

(i). Considering grade C or above as a pass grade, how many students from this data successfully passed the course?

(ii). Considering grade C or above as a pass grade, what is the probability for a student to receive a pass grade?

(iii). What is the probability for a student not receiving a pass grade?

(iv). What is the probability that the student received grade A or grade B?

(v). What is the probability that the student received grade A, grade B, or grade C?

(vi). Do you consider the events in the previous question as mutually exclusive events? Yes No Maybe

(vii). What is the probability that a student received grade A and grade B?

Answer 1

Given the data, we have 7 students who received grade A, 2 student received grade B, 1 students received grade C, 0 students received grade D and 1 student received grade F.

i)

Considering grade C or above as a pass grade - 10 out of 11 students have successfully passed the course.

ii)

Considering grade C or above as a pass grade, the probability for a student to receive a pass grade

=Probability of receiving either an A or B or C

= 1/5 + 1/5 + 1/5 = 3/5 (disjoint events)

iii)

Probability for a student not receiving a pass grade = 1 - Probability of receiving a pass grade = 1 -3/5 = 2/5

iv)

Probability that the student received grade A or grade B = Prob of receiving A + Prob of receiving B

= 1/5 + 1/5 = 2/5

v)

Probability that the student received grade A, grade B, or grade C = Prob of receiving A + Prob of receiving B+Prob of receiving C = 1/5 + 1/5 +1/5 = 3/5

vi)

Yes, the events in the previous question are mutually exclusive events. In probability theory, two events are mutually exclusive or disjoint if they cannot both occur at the same time.

vii)

Probability that a student received grade A and grade B =

(Mutually exclusive events)