Question

An instructor ahs a question bank consisting of 300 easy true / false question, 200 difficult true/false question , 500 easy multiple choice questions and 400 difficult multiple choice questions. IF a question is selected at random from the test bank, what is the probability that it will be an easy question g9iven that it is a multiple choice question?

Answer 1

Tota number of question = 300+200+500+400 = 1400.
LEt E be the event that selected question is an easy question
Then $n\left(E\right)=500+300=800\therefore P\left(E\right)=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}=\frac{800}{1400}=\frac{4}{7}$
LEt F be the event that selected question is a multiple choice question.
Then, $n\left(F\right)=500+400=900\therefore P\left(F\right)=\frac{Totalnumberofeasyquestiions}{Totalnumberofquestion}=\frac{900}{1400}=\frac{9}{14}\therefore P(E\cap F)=\frac{500}{1400}=\frac{5}{14}\therefore P\left(\frac{E}{F}\right)=\frac{P(E\cap F)}{P\left(F\right)}=\frac{\frac{5}{14}}{\frac{9}{9}}$