Question

The percentage of marks obtained by a student in the monthly unit test are given as

Unit test:	1	2	3	4	5
Percentage of marks obtained:	60	75	55	72	85

Find the probability that, students get at least 60% marks.

Answer 1

Hint: We are asked to find probabilities. We firstly find the sample space S. Sample will consist of all possible outcomes as our event in students getting at least 60% marks. So, S will be the all possible % of marks obtained by marks. Once we have S we will look to find the size of S as the size of S will tell us the total possible outcome. After this, we will find total favorable outcomes (outcomes that are greater than 60%) once, we have these two, we will use \[\text{Probabilities}=\dfrac{\text{Total favorable outcome}}{\text{Total possible outcome}}\] to get our answer.

Complete step by step answer:

We are given that, a monthly unit test has happened and the percentage of marks are given to us. A total of 5 tests were taken place and the percentage of marks in those tests are 60, 75, 55, 72, and 85.
So, sample space for us becomes:
\[S=\left\{ 60,75,55,72,85 \right\}\]
Sample space is the collection of all possible outcomes that can occur when an event happens. As we have that when test happened the percentage of marks obtained are 60, 75, 55, 72 and 85. So, these numbers will make our sample space. Hence our sample space is
\[S=\left\{ 60,75,55,72,85 \right\}\]
A total of 5 elements are there in the sample space. So, \[\text{n}\left( \text{S} \right)=\text{5}\]
Now, we know the probability of an event is given as the ratio of a favorable outcome to the total possible outcomes. So,
\[\text{Probabilities}=\dfrac{\text{Number of favorable outcome of event E}}{\text{Total number of possible outcome}}\]
We are asked to find the probabilities that students will get at least 60% marks.
So, from our sample space \[S=\left\{ 60,75,55,72,85 \right\}\]. As at least means greater than or equal to, so our favorable outcome consists of a number that is more than or equal to 60. So, our favorable outcomes are 60, 75, 72, and 85.
So the number of favorable outcome = 4
As our sample space size n (5) is 5. So, the total number of possible outcomes is 5.
Now, we will use this value in formula of probability.
\[\text{Probabilities}=\dfrac{\text{Number of favorable outcome of event E}}{\text{Total number of possible outcome}}\]
We get,
\[P\left( \text{at least 60} \right)=\dfrac{4}{5}\]
As $\dfrac{4}{5}$ cannot be simplified. So, we get,
\[P\left( \text{students get at least 60 }\!\!\%\!\!\text{ } \right)=\dfrac{4}{5}\]

Note:
 Remember, at least x describes the condition when we are having the right to choose n as well other which are greater than x. So, that’s why at least 60% means, the percentage must be 60 or more than 60, so while choosing a favorable outcomes, we will choose 60 as well and this will make our number of a favorable outcome as y. Remember, the probability is always expressed into the simplest whole-number ratio. So we always check if it can be simplified more or not.