Answer:a. To find out how many students chose both games, we can add the number of students who chose cricket and the number of students who chose hockey, and then subtract the total number of students who chose at least one sport.
Number of students who chose both games = Number of students who chose cricket + Number of students who chose hockey - Number of students who chose at least one sport
Number of students who chose both games = 45 + 52 - 64
Number of students who chose both games = 33
Therefore, 33 students chose both cricket and hockey.
b. To find out how many students chose cricket only, we can subtract the number of students who chose both games from the total number of students who chose cricket.
Number of students who chose cricket only = Number of students who chose cricket - Number of students who chose both games
Number of students who chose cricket only = 45 - 33
Number of students who chose cricket only = 12
Therefore, 12 students chose cricket only.
c. To find out how many students chose hockey only, we can subtract the number of students who chose both games from the total number of students who chose hockey.
Number of students who chose hockey only = Number of students who chose hockey - Number of students who chose both games
Number of students who chose hockey only = 52 - 33
Number of students who chose hockey only = 19
Therefore, 19 students chose hockey only.
d. To find out how many students chose neither cricket nor hockey, we can subtract the number of students who chose at least one sport from the total number of students.
Number of students who chose neither cricket nor hockey = Total number of students - Number of students who chose at least one sport
Number of students who chose neither cricket nor hockey = 80 - 64
Number of students who chose neither cricket nor hockey = 16
Therefore, 16 students chose neither cricket nor hockey.
