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		Low	Average	High
	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

Answer 1

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.
$n\left(E_4\right)=25$ i.e. $m_4=25$
$P\left(E_4\right)=\frac{m_4}{n}=\frac{25}{200}=\frac{1}{8}$