the marks scored by some students in an examination (out of 1000) are given below in the form of a frequency distribution table:
Marks 500-600 600-700 700-750 750-800 800-850 850-950 950-1000
no:of students 25 30 150 240 150 50 15
if a student is selected at random , find the probability that the student scored:
(i)less than 750 marks
(ii)less than 50%marks
(iii)marks between 75% and 95%

Answer :

The marks scored by some students in an examination (out of 1000) are given below in the form of a frequency distribution table:
 

Marks	500 - 600	600 - 700	700 - 750	750 - 800	850 - 900	900 - 950	950 - 1000
Number of students	25	30	150	240	150	50	15

And

We know Probability P ( E ) = $\frac{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{desired} \mathrm{events} \mathrm{n} ( \mathrm{E} )}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{events} \mathrm{n} ( \mathrm{S} )}$

Here Total number of students  = 25 + 30 + 150 + 240 + 150 + 50 + 15  =  660
So,
if a student is selected at random , find the probability that the student scored:
n ( S ) =  660 

i ) Less than 750 marks
So,
n ( E ) =  25 +  30 +  150  =  205
So,
Probability P ( E ) = $\frac{205}{660} = \frac{\mathbf{41}}{\mathbf{132}} ( \mathrm{Ans} )$

ii )  we know total marks  =  1000  , So 50% of marks  =  50% of 1000 = $\frac{50 \times 1000}{100} = 500$
And
Students get less than 500 marks  =   0 (  As there  is no information about number of students getting less than 500 marks )
So,
n (  E ) = 0
So,
Probability P ( E ) = $\frac{0}{660} = \mathbf{0} ( \mathrm{Ans} )$

iii ) we know total marks  =  1000  , So 75% of marks  =  75% of 1000 = $\frac{75 \times 1000}{100} = 750$
And
95% of marks  =  95% of 1000 = $\frac{95 \times 1000}{100} = 950$
So,
Total number of students getting marks in between 750 and 950 = 240 + 150 + 50 =  440

n ( E ) =  440

So,
Probability P ( E ) = $\frac{440}{660} = \frac{\mathbf{2}}{\mathbf{3}} \mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$