Answer to Question #297773 in Statistics and Probability for kool

Question

There are a total of 180 students who are part of badminton, table tennis and tennis team of the college. Of which 70% of students play table tennis, 10% play tennis and 60% play badminton. It is also noticed that all students who play tennis also play table tennis but not badminton. Now a student is selected at random, what is the probability that he/she is the part of table tennis team only?

Answer 1

There are$180(0.1)=18$ students who play tennis.

Let $x=$ the number of students who play table tennis and badminton.

Then there are $180(0.7)-18-x=108-x$ students who play table tennis only.

There are $180(0.6)-x=108-x$ students who play badminton only.

$$18+108-x+108-x+x=180$$

$$x=54$$

There are$108-54=54$ students who play tennis only.

The probability that he/she is the part of table tennis team only is

$$P(tennis \ only)=\dfrac{54}{180}=0.3$$