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In a college 40 % students attend Mathematics class, 30% students attend physics class and 20% students attend both the classes, If a student is chosen at random from the college, the probability that the student chosen attend only one class is

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a

$\frac{3}{10}$

b

$\frac{1}{3}$

c

$\frac{2}{3}$

d

$\frac{1}{4}$

answer is A.

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Detailed Solution

A=Student attend MATHS Class

B=Student attend Physics class

$\begin{array}{rcl} P (A) & = & \frac{40}{100}, \end{array}$ $\begin{array}{rcl} P (B) & = & \frac{30}{100}, \end{array}$ $\begin{array}{rcl} P (A \cap B) & = & \frac{20}{100} \end{array}$

$\begin{array}{rcl} P (A \cap B) + P (A \cap B) \\ = & P (A) - P (A \cap B) + P (B) - P (A \cap B) \\ = & \frac{40}{100} + \frac{30}{100} - 2 (\frac{20}{100}) = \frac{3}{10} \end{array}$

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