Total Students Calculation
This problem involves calculating the total number of students using provided percentages for sports participation and the count of non-participants.
Student Participation Percentages
The given data is:
- Only Cricket: 30%
- Only Football: 20%
- Only Basketball: 10%
- Both Football & Cricket (Intersection): 20%
- Both Basketball & Cricket (Intersection): 15%
- Both Football & Basketball (Intersection): 10%
- All Three Games: 5%
- No Games: 15 students
Players Percentage Sum
We calculate the sum of percentages for distinct groups playing at least one game:
- Only Cricket: 30%
- Only Football: 20%
- Only Basketball: 10%
- Cricket and Football only (excluding all three): $20\% - 5\% = 15\%$
- Basketball and Cricket only (excluding all three): $15\% - 5\% = 10\%$
- Football and Basketball only (excluding all three): $10\% - 5\% = 5\%$
- All Three Games: 5%
Total percentage of students playing at least one game = $30\% + 20\% + 10\% + 15\% + 10\% + 5\% + 5\% = 95\%$
Non-Players Percentage
The percentage of students playing no games is calculated as:
$100\% - (\text{Percentage playing at least one game}) = 100\% - 95\% = 5\%$
Final Total Students
We are given that 15 students play no games. This 15 corresponds to the 5% calculated above.
Let '$T$' represent the total number of students.
The equation is:
$ 5\% \times T = 15 $
Converting percentage to a fraction:
$ \frac{5}{100} \times T = 15 $
Solving for '$T$':
$ T = 15 \times \frac{100}{5} $
$ T = 15 \times 20 $
$ T = 300 $
Thus, the total number of students is 300.
Important Questions from Set Theory and Venn Diagram (Notes)
Match List-I with List-II
List-1 List-II (A) If X and Y are two sets such that n(X)= 17, n(Y)=23, n(X $\cup$ Y)=38, then n(X $\cap$ Y) is (I) 20 (B)) If n(X) = 28,n(Y) = 32,n(X$\cap$Y) = 10, then n(X$\cup$Y) is (II) 10 (C) If n(X) = 10, then n(7X) is (III) 50 (D) If n(Y) = 20, then n($\frac{Y}{2}$) is (IV) 2 Choose the Correct answer from the options given below:
- From the given sets, which is an infinite set:
1. {x: x $\in$ N and (x-1)(x-2) = 0}
2. {x: x $\in$ N and x is prime number and less than 199}
3. {x: x $\in$ N and x$^5$ - 1 = 0}
4. {x: x $\in$ N and x is odd} Consider the following relation R={(4,5),(5,4), (7,6),(6,7)} on set I={4,5,6,7}. Which of the following properties relation R does not have?
A. Reflexive property
B. Symmetric property
C. Transitive property
D. Antisymmetric property
Choose the correct answer from the options given below:Find the least upper bound and greatest lower bound of $S=\{X,Y,Z\}$ if they exist, of the poset whose Hasse diagram is shown below:
- In a class, 40 like Math, 35 like Science, 30 like English; 15 like both Math and Science, 12 like Math and English, 10 like Science and English, 5 like all three. How many like atleast one?
