The marks obtained by a student in five tests are as follows:
Test Number Marks obtained $1$ $62$ $2$ $72$ $3$ $78$ $4$ $91$ $5$ $85$
If one of the tests is chosen at random,find the probability that the student scored $(1)$ more than $90$ marks and $(2)$ between $70$ and $80$ marks in that test.
| Test Number | Marks obtained |
| $1$ | $62$ |
| $2$ | $72$ |
| $3$ | $78$ |
| $4$ | $91$ |
| $5$ | $85$ |
If one of the tests is chosen at random,find the probability that the student scored $(1)$ more than $90$ marks and $(2)$ between $70$ and $80$ marks in that test.
(N/A) Total number of tests = $5$.
$(1)$ Number of tests where the student scored more than $90$ marks is $1$ (Test $4$ with $91$ marks).
Therefore,the probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{5}$.
$(2)$ Number of tests where the student scored between $70$ and $80$ marks is $2$ (Test $2$ with $72$ marks and Test $3$ with $78$ marks).
Therefore,the probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{5}$.
$(1)$ Number of tests where the student scored more than $90$ marks is $1$ (Test $4$ with $91$ marks).
Therefore,the probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{5}$.
$(2)$ Number of tests where the student scored between $70$ and $80$ marks is $2$ (Test $2$ with $72$ marks and Test $3$ with $78$ marks).
Therefore,the probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{5}$.
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