Answer to Question #124333 in Statistics and Probability for Yasini

Question

John noticed that his director is happy on 60% of his calls,so he assign a probability of his being happy on his visit as 0.6. he also noticed that if he is happy, he accedes to his request with a probability of 0.4 where as if he is not happy he accedes to the request with probability of 0.1. John called one day and the director accedes to john&'s request. What is the probability that is was happy?

Answer 1

This is a conditional probability which is given by the formulae p(a/b)= p(a & b)/p(b)

thus let h is happy, a acceded p(a/h)= p(a&h)/p(h), 0.4= (p(a & h)/0.6 , p(a&h)= 0.6*0.4= 0.24

Now for we know p(a/h)= 0.4, p(a&h) = 0.24 thus we can calculate p(h) using the formulae

p(a/h)= p(a&h)/p(h), 0.4 = 0.24/p(h) , p(h) = 0.24/0.4 = 0.6 thus the probability that he was happy is 0.6