There are a total of 220 students who are part of badminton, table tennis and tennis team of the college. Of which 50% of students play table tennis, 30% 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(Enter the answer correct to 1 decimal place) probability that he/she is the part of table tennis team only?
Question
There are a total of 220 students who are part of badminton, table tennis and tennis team of the college. Of which 50% of students play table tennis, 30% 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(Enter the answer correct to 1 decimal place) probability that he/she is the part of table tennis team only?
Solution
First, let's break down the information given:
- Total students = 220
- Students who play table tennis = 50% of 220 = 110
- Students who play tennis = 30% of 220 = 66
- Students who play badminton = 60% of 220 = 132
It is mentioned that all students who play tennis also play table tennis but not badminton. So, these 66 students are included in the 110 table tennis players.
Therefore, the number of students who play only table tennis = Total table tennis players - Players who play both tennis and table tennis = 110 - 66 = 44
The probability of a student being part of the table tennis team only is calculated as the number of favorable outcomes (students who only play table tennis) divided by the total number of outcomes (total students).
So, the probability = 44 / 220 = 0.2
Therefore, the probability that a student selected at random is part of the table tennis team only is 0.2 or 20%.
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