Question

The following are the marks obtained by students in maths with grade in a school. Find the probability of getting a D grade.

Mark	$ 0 - 33 $	$ 34 - 50 $	$ $ $ 51 - 65 $	$ $ $ 66 - 80 $	$ 80 - 100 $	$ $ Total
No. of student	$ 06 $	$ 16 $	$ 40 $	$ 8 $	$ 10 $	$ 80 $
Grade	$ F $	$ D $	$ C $	$ B $	$ A $

A. $ \dfrac{1}{5} $
B. $ \dfrac{1}{2} $
C. $ \dfrac{1}{8} $
D. $ \dfrac{1}{{10}} $

Answer 1

Hint: This type of question will be solved by using the probability formula. Probability of occurrence of any event is the ratio of number of outcomes in that event to the total number of possible outcomes.

Complete step-by-step answer:
Observe the table

Mark	0-33	34-50	51-65	66-80	80-100	Total
No. of student	06	16	40	8	10	80
Grade	F	D	C	B	A

We have to find the probability of getting a D grade.
The number of students who are getting D grades are 16.
The total number of students in the school are
  $ 6 + 16 + 40 + 8 + 10 = 80 $
Here, D is the event and school is a sample space that contains all possible outcomes.
Basic probability theorems state that probability of any event is the ratio of the number of elements in the event to the total number of possible outcomes.
Therefore,
$\Rightarrow{\text{ Probability of getting D grade}} =\dfrac{\text{No of student who got D grade}}{\text{ total number of students in school}}$
Put the given value in above of formula
Then, probability of getting $ D $ grade
 $ = \dfrac{{16}}{{80}} $
 $ = \dfrac{1}{5} $
Therefore, from the above explanation, the correct answer is (A) $ \dfrac{1}{5}
So, the correct answer is “Option A”.

Note: Since, the number of elements in an event is always less than the number of elements in sample space, the probability can never be greater than 1. And since, ‘number of elements’ is a positive quantity, probability can never be negative.