Test results of three different courses from 100 samples are

Test results of three different courses from 100 samples are summarized as follows: Successful? Let A denote the event that a sample is from course 1, and let B denote the event that a sample is successful. Are events A and B independent? Why, Why not? Determine (A|B) and (B|A).

Solution

P(A) = P(Sample is from course 1) = (22+8)/100 = 30 /100 = 0.3

P(B) = P( Sample is successful) = (22+25+30) / 100 = 77/100= 0.77

A,B are independent when P(A n B) = P(A) * P(B)

P( A n B) = P( Sample is from course 1 and successful) = 22/100 = 0.22

P(A) * P(B) = 0.77*0.3 = 0.231

it is not independent

b)
P(A|B) = P ( A n B) / P(B) = 0.22 / 0.77 = 0.2857

P(B|A) = P ( A n B) / P(A) = 0.22 / 0.30 = 0.7333