A teacher wanted to analysis the performance of two sections of students in a mathematics test of 100 marks. Looking performance, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows :
0-20, 20-30, ....., 60-70, 70-100. Then she formed the following table :
`|{:("Marks"," Number of students"),(0-20," 7"),(20-30," 10"),(30-40," 10"),(40-50," 20"),(50-60," 20"),(60-70," 15"),(70-"above"," 8"),("Total"," 90"):}|`
(i) Find the probability that a student obtained less than `20%` in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above .

Explanation

(i) Total number of student in a class, `n(S) = 90`
The number of student obtained less than `20%` marks lies in the interval `0-20`, i.e., `n(E) = 7`
`therefore` The probability, that a student obtained less than `20%` marks in the methematics test
`=(n(E))/(n(S))=(7)/(90)`
(ii) The number of students obtained marks 60 or above lies in the marks interval 60-70 and 70-above, i.e., `n(F)=15+8=23.`
`therefore` The probability that a student obtained marks 60 or above `=(n(F))/(n(S))=(23)/(90)`