The percentages of marks obtained by a student in six unit tests are given below.

Unit test I II III IV V VI

Percentage of marks obtained 53 72 28 46 67 59

A unit test is selected at random. What is the probability that the student gets more than 60% marks in the test?

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Solution

Total number of unit tests = 6
Number of tests in which the student scored more than 60% marks = 2
Let E be the event that he got more than 60% marks in the unit tests.Then,

required probability = P(E) = $\frac{Number of unit tests in which he got more than 60 % marks}{Total number of unit tests} = \frac{2}{6} = \frac{1}{3}$

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The percentages of marks obtained by a student in six unit tests are given below:

If a test is selected at random then, the probability that the student gets more than 60% marks in the test is

The percentage of marks obtained by a student in monthly unit tests are given below:

$\begin{matrix} unit test & I & I I & I I I & I V & V Percentage of marks obtained & 69 & 71 & 73 & 68 & 76 \end{matrix}$

Find the probability that the student gets:

(i) more than 70% marks (ii) less than 70% marks (iii) a distinction.

Test	$I$	$I I$	$I I I$	$I V$	$V$
Percentage marks obtained	$69$	$71$	$73$	$69$	$74$

70 %

Marks	4	12	20	28	36	44
Number of students	8	10	16	24	15	7

Marks	0−20	20−40	40−60	60−80	80−100
No. of students	8	15	32	26	9

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Unit test	I	II	III	IV	V	VI
Percentage of marks obtained	53	72	28	46	67	59