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June 2020 p52 q2
2577
A total of 500 students were asked which one of four colleges they attended and whether they preferred soccer or hockey. The numbers of students in each category are shown in the following table.
Soccer
Hockey
Total
Amos
54
32
86
Benn
84
72
156
Canton
22
56
78
Devar
120
60
180
Total
280
220
500
Find the probability that a randomly chosen student is at Canton college and prefers hockey.
Solution
The number of students at Canton college who prefer hockey is 56, as shown in the table.
The total number of students surveyed is 500.
The probability that a randomly chosen student is at Canton college and prefers hockey is given by the ratio of the number of Canton hockey students to the total number of students:
\(\text{Probability} = \frac{56}{500}\)
This fraction can be simplified to \(\frac{14}{125}\).
Alternatively, the decimal form of the probability is 0.112.