There are a total of 220 students who are part of badminton, table tennis and tennis team of the college. Of which 60% of students play table tennis, 20% play tennis and 70% 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?(Enter the answer correct to 1 decimal place
Question
There are a total of 220 students who are part of badminton, table tennis and tennis team of the college. Of which 60% of students play table tennis, 20% play tennis and 70% 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?(Enter the answer correct to 1 decimal place
Solution
First, let's find out how many students play each sport:
- Table Tennis: 60% of 220 = 0.60 * 220 = 132 students
- Tennis: 20% of 220 = 0.20 * 220 = 44 students
- Badminton: 70% of 220 = 0.70 * 220 = 154 students
From the problem, we know that all students who play tennis also play table tennis but not badminton. So, the 44 students who play tennis are included in the 132 students who play table tennis.
Therefore, the number of students who play only table tennis is: 132 (total table tennis players) - 44 (tennis players who also play table tennis) = 88 students.
The probability that a student selected at random is part of the table tennis team only is therefore 88 (students who only play table tennis) divided by 220 (total students), or 88/220 = 0.4.
So, the probability is 0.4 or 40%.
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