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, then the probability that it will be an easy question given that it is a multiple choice question, is

• A. $\frac{2}{9}$
• B. $\frac{1}{9}$
• C. $\frac{4}{9}$
• D. $\frac{5}{9}$

Answer 1

Answer: (D)

Total number of questions
$=300+200+500+400$
$=1400$
Let $E$ be the event that selected question is an easy question.
Then, $n(E)=500+300=800$
$\therefore P(E)=\frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }}$
$=\frac{800}{1400}=\frac{4}{7}$
Let $F$ be the event that selected question is a multiple choice question.
Then,$n(F)-500+400-900$
$\therefore P(F)=\frac{\text{ Number of multiple choice questions }}{\text{ Total number of questions }}$
$=\frac{900}{1400}=\frac{9}{14}$
$\therefore P(E\cap F)=\frac{500}{1400}=\frac{5}{14}$
$\therefore P\left(\frac{E}{F}\right)=\frac{P(E\cap F)}{P(F)}=\frac{5/14}{9/14}=\frac{5}{9}$