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 ) = Total number of desired events n ( E )Total number of events n ( 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 ) = 205660 = 41132                    ( Ans )

ii )  we know total marks  =  1000  , So 50% of marks  =  50% of 1000 = 50 × 1000100 = 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 ) = 0660 = 0                    ( Ans )

iii ) we know total marks  =  1000  , So 75% of marks  =  75% of 1000 = 75 × 1000100 = 750
And
95% of marks  =  95% of 1000 = 95 × 1000100 = 950
So,
Total number of students getting marks in between 750 and 950 = 240 + 150 + 50 =  440

n ( E ) =  440

So,
Probability P ( E ) = 440660 = 23                    ( Ans )

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Hope it helps:-

Total obs. = 1000.
1) P ( less than 750 mks ) = 25 + 30 + 150 = 205 / 1000 = 0.205.
2) P ( less than 50% ) = same = 0.205.
3) P ( 75% - 95% ) = 150 + 50 / 1000 = 200 / 1000 = 1 / 5 or 0.2.

Have a good day..!!!!
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