Question

In a class of 50 students, every student needs to choose at least one outdoor sport. There are 3 outdoor sports, football, baseball, and soccer. Find the percentage of people who choose all the three sports.

• A. 10%
• B. 42%
• C. 50%
• D. 5%

Answer 1

The correct option is A 10%

In the Venn diagram, we have:
Here, $A\bigcap B$ indicates the common elements in both sets A and B. The same goes for $B\bigcap C$ and $A\bigcap C$.

$A\bigcap B\bigcap C$ indicates the elements common in the sets A, B, and C.


From the Venn diagram, it is clear that 15 students like only football, 12 students like only baseball, 13 students like only soccer, 22 students like both football and baseball, 15 students like both football and soccer, 10 students like both baseball and soccer, and only 5 students like all the three sports.

Total number of students = 50

Number of students choosing all three sports = 5

$\text{Percentage of students choosing all three sports}$
$=\frac{\text{Number of students choose all 3 sports}}{\text{Total number of students}}\times 100$

$⟹\frac{5}{50}\times 100=10$%