Question

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
8 students who received grade A,
2 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:

Considering grade C or above as a pass grade, how many students from this data successfully passed the course?
Considering grade C or above as a pass grade, what is the probability for a student to receive a pass grade?
What is the probability for a student not receiving a pass grade?
What is the probability that the student received grade A or grade B?
What is the probability that the student received grade A, grade B, or grade C?
Do you consider the events in the previous question as mutually exclusive events?	---------   Yes   No   Maybe
What is the probability that a student received grade A and grade B?
What is the probability that a student received grade A, i.e., P(A) is:
What is the probability that a student received grade B, i.e., P(B) is:
What is the probability that a student received grade C, i.e., P(C) is:
What is the probability that a student received grade D, i.e., P(D) is:
What is the probability that a student received grade F, i.e., P(F) is:
What is the expected value of these grades?
What is the variance of these grades?

Answer 1

SOLUTION

MARKS	GRADES
105 91	A A
82	B
86	B
100	A
96	A
98	A
109	A
96	A
95	A
57	F

Since there are 11 students whose marks and respective grades have been shown in the table, we have 8 student having A grade, 1 students having F grade and 2 student having grade B.

i) Considering grade C or above as a pass grade, according to this data, 9 students have successfully passes the course.

ii) Probability= No. of favorable outcomes/ Total no. of outcomes

= 10/11

iii) Probability for a student not receiving a pass grade( i.e. C or above) = 1- Probability for a student receiving a pass grade

= 1- (10/11)

= 1/11

iv) Probability that a student received A grade= 8/11

Probability that a student received B grade= 2/11

Probability that a student received A or B = (8/11) + (2/11)

= 10/11 (Since 'or' represents addition of the probabilities)

v) Following the similar notion here,

Probability that a student received C grade = 0/11 =0

Taking probabilities of A and B from part (iv)

Probability that the student received grade A, grade B, or grade C= (8/11) + (2/11) + (0)

= 10/11

vi) Yes, the events in part (v) are mutually exclusive events. This is because mutually exclusive events are those events which cannot occur simultaneously or at the same time. This means that in this case, a student cannot be awarded grade A and grade B at the time. He will get either grade A or grade B or grade C at a time.

vii) Probability that a student received A grade= 8/11

Probability that a student received B grade= 2/11

Probability that a student received grade A and grade B = (8/11) * (2/11) ( Since 'and' represents multiplication of the probabilities).

= 16/121 = 0.1333(approx)