Question

One hundred management students who read at least one of the three business magazines are surveyed to study the readership pattern. It is found that 80 read Business India, 50 read Business World and 30 read Business Today. Five students read all the three magazines. A student was selected randomly. Find the probability that he reads exactly two magazines.

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. None of these

Answer 1

The correct option is B $\frac{1}{2}$

Let $P\left(I\right),P\left(W\right)$ & $P\left(T\right)$ denote the probability of student reads Business India, Business world & Business today

$P\left(I\right)=\frac{80}{100},P\left(W\right)=\frac{50}{100},P\left(T\right)=\frac{30}{100}$

Probability that student reads exactly two

$P(I\cap W)+P(I\cap T)+P(W\cap T)3P(I\cap W\cap T)$

$=P\left(I\right)+P\left(W\right)+P\left(T\right)+P(I\cap W\cap T)13P(I\cap W\cap T)$

$=\frac{80}{100}+\frac{50}{100}+\frac{30}{100}-1-\frac{10}{100}=\frac{50}{100}=\frac{1}{2}$