In a survey 120 students 60 only have a stereo 40 only have

In a survey 120 students. 60 only have a stereo. 40 only have a computer. 15 have both. 5 have neither. What is the probability that a student selected at random has a stereo given that the student does not have a computer?

Solution

P(stereo only) = 60/120 = 1/2 = 0.50

P(computer only) = 40/120 = 1/3 = 0.333

P( stereo and computer) = 15/120 = 0.125

P( neither stereo and computer ) = 5/120 =0.04167

P(Computer) = 0.333 + 0.125 = 0.458

P( Student does \'t have a computer) = 1 - 0.458 = 0.542

P( stereo and does \'t have a computer) = P( stereo only) = 0.50

P(student selected at random has a stereo given that the student does not have a computer) = P( stereo and does \'t have a computer) / P( Student does \'t have a computer) = 0.50/0.542=0.9225