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?

Solution

The given data is

	Easy	Difficult	Total
True/False	300	200	500
Multiple Choice	500	400	900
Total	800	600	1400

Let E : Easy questions, D : Difficult questions
T : True/false questions and M : Multiple choice questions
Number of easy multiple choice questions = 500
Total number of questions = 1400
$straight P left parenthesis straight E intersection straight M right parenthesis$ = Probability of selecting an easy and multiple choice question
$equals space 500 over 1400$
Total number of multiple choice questions
= 500 + 400 = 900
P(M) = Probability of selecting one multiple choice question
$equals space 900 over 1400$
$straight P left parenthesis straight E space left enclose straight M right parenthesis space equals space fraction numerator straight P left parenthesis straight E intersection straight M right parenthesis over denominator straight P left parenthesis straight M right parenthesis end fraction space equals fraction numerator begin display style 500 over 1400 end style over denominator begin display style 900 over 1400 end style end fraction space equals 5 over 9$

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