Venn Diagrams

In a group of $30$ people, $10$ of them like to read Indian Express, $15$ of them like to read Financial Express. If $30\%$ of people do not like to read at all, then how many people like to read both i.e. Indian Express and Financial Express.

In a group of $75$ tourists, $25$ visited only Kolkata and $23$ visited only Mumbai. How many visited both the places?

In a group of $75$ tourists, $25$ visited only Kolkata and $23$ visited only Mumbai. How many visited Kolkata?

In a group of $50$ persons who speak English or Tamil or both, $37$ speak English and $30$ speak Tamil. How many speak only Tamil?

Given, $n\left(\xi \right)=50, n\left(A\right)=28, n\left(B\right)=20, n(A\cap B)=3$. Hence find $n(\mathrm{A}\cup \mathrm{B}).$

If $n\left(\xi \right)=50, n\left(A\right)=28, n\left(B\right)=20, n(A\cap B)=3$, then $n\left(\mathrm{B}\text{ only }\right)=$_____.

Given, $n\left(\xi \right)=50, n\left(A\right)=28, n\left(B\right)=20, n(A\cap B)=3$. The value of $n\left[(\mathrm{A}\cup \mathrm{B})\text{'}\right]$ is _____.

In a class of $40$ students, $23$ play hockey and $30$ play cricket. _____ plays both the games ?

The set represented by the shaded region in the Venn-diagram is $A-B$.

The set represented by the shaded region in the Venn-diagram is $(A-B)\cup (B-A)$. _____

$(A\cup$_____$)\text{'}$ is the set represented by the shaded region in the Venn-diagram:

In a group of $40$ girls, $35$ like cashew nuts, $18$ like groundnuts and $2$ do not like both nuts. The number of girls like only cashew nuts are _____.

In a group of $50$ persons who speak English or Tamil or both, $37$ speak English and $30$ speak Tamil. How many speak both the languages?

In a group of $50$ persons who speak English or Tamil or both, $37$ speak English and $30$ speak Tamil. How many speak only English?

In a city, $50\%$ people read newspaper $A, 45\%$ read newspaper $B$, and $25\%$ read neither $A$ nor $B$. Percentage of people read both the newspapers $A$ as well as $B$ is $k\%$. Now, find the value of $k$.

Given $A=$ {students who like cricket} and $B=$ {students who like tennis}; $n\left(A\right)=20, n\left(B\right)15$ and $n\left(A\cap B\right)=5$. Illustrate this through a Venn diagram and then find $n\left(A\cup B\right)$.

In a town of $840$ persons, $450$ persons read Hindi, $300$ read English and $200$ read both. Then the number of person who read neither is

In a class of $200$ students who appeared certain examinations, $35$ students failed in CET, $40$ in NEET, $40$ in JEE, $20$ failed in CET and NEET, $17$ in NEET and JEE, $15$ in CET and JEE and $5$ failed in all the three examinations. Find how many students did not fail in any examination. 

For two events A and B, the probability that both the events occur simultaneously is equal to $\frac{1}{4}$ and the probability that none of the events occur is $\frac{1}{3}$. Then, the probability that exactly one of A or B occurs is equal to

If $\mu =\{0,1,2,3,4,5,6,7,8,9,10\}, A=\{2,3,5,8\}$ and $B=\{0,3,5,7,10\}$. Then, the correct representation of $A\cap B$ in the Venn diagram will be: