Question

An instructor has a question bank consisting of $300$ easy True / False questions, $200$ difficult True / False questions, $500$ easy multiple choice questions and $400$ difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question ?

Answer 1

The given data can be tabulated as

Let us denote $E=$ easy questions, $M=$ multiple choice questions, $D=$ difficult questions, and $T=$ True / False questions.

Total number of questions $=1400$

Total number of multiple choice questions $=900$

Therefore, probability of selecting an easy multiple choice questions is

$P(E\cap M)=\frac{500}{1400}=\frac{5}{14}$

Probability of selecting a multiple choice questions, $P\left(M\right)$ is $\frac{900}{1400}=\frac{9}{14}$

$P\left(E|M\right)$ represents the probability that a randomly selected question will be an easy question, given that it is a multiple choice question.

$P\left(E|M\right)=\frac{P(E\cap M)}{P\left(M\right)}=\frac{\frac{5}{14}}{\frac{9}{14}}=\frac{5}{9}$

Therefore, the required probability is $\frac{5}{9}$