Question

of the total no. of 200 students appearing in an examination 140 passed i n mathematics and 100 passed in statistics if 40 of them failed in both find the percentage of studendts who have passed in both​

Answer 1

Answer:  40% of the students passed in both the subjects.

Step-by-step explanation:  Given that the total number of students appearing in an examination is 200 out of which 140 passed in Mathematics, 100 passed in Statistics and 40 failed in both the subjects.

We are to find the percentage of students who have passed in both the subjects.

Let A and B represents the set of students who have passed in Mathematics and Statistics respectively.

Then, according to the given information, we have

$n(A)=140,~~n(B)=100,\\\\200-n(A\cup B)=40\\\\\Rightarrow n(A\cup B)=200-40\\\\\Rightarrow n(A\cup B)=160,\\\\\\n(A\cap B)=?$

From set theory, we have

$n(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\\Rightarrow n(A\cap B)=n(A)+n(B)-n(A\cup B)\\\\\Rightarrow n(A\cap B)=140+100-160\\\\\Rightarrow n(A\cap B)=80.$

Therefore, the percentage of students who have passed in both he subjects is given by

$p=\dfrac{n(A\cap B)}{200}\times100\%=\dfrac{80}{200}\times100\%=40\%.$

Thus,40% of the students passed in both eh subjects.