Answer to Question #240176 in Statistics and Probability for mickey

Question

A family has two dogs (Rex and Rover) and a cat called Garfield. None of them is fond of the postman. If

they are outside, the probability that Rex, Rover and Garfield will attack the postman are 30%, 40% and

15%, respectively. Only one is outside at time, with probabilities 10%, 20% and 70%, respectively.

If the postman is attacked, what is the probability that Rex was the culprit?

Answer 1

$P(Rex)=\frac{0.3*0.1}{0.3*0.1+0.4*0.2+0.15*0.7}=\frac{0.03}{0.215}\approx 0.1395.$