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Question

A researcher would like to determine whether there is a relationship between a students interest in statistics and his or her ability in mathematics. A random sample of $$200$$ students is selected and they are asked whether their ability in mathematics and interest in statistics is low, average or high. The results were as follows:
Ability in mathematics
Interest in statistics
LowAverageHigh
Low$$60$$$$15$$$$15$$
Average$$15$$$$45$$$$10$$
High$$5$$$$10$$$$25$$
If a student is selected at random, what is the probability that he / she has high ability in mathematics and high interest in statistics


Solution

Total number of students $$= 80 + 70 + 50 = 200$$. i.e. $$n = 200$$
Let $$E_{4}$$ be the event has high ability in mathematics and high interest in statistics.
$$n(E_{4}) = 25$$ i.e. $$m_{4} = 25$$
$$P(E_{4}) = \dfrac {m_{4}}{n} = \dfrac {25}{200} = \dfrac {1}{8}$$

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