Two computer programs are designed to perform certains tasks. Each time you have a new task, you make both programs handle it, and then check which of the two works better. You are aware that one of...

Two computer programs are designed to perform certains tasks. Each time you have a new task, you make both programs handle it, and then check which of the two works better. You are aware that one of the programs outperforms the other in 60 percent of the cases and underperforms in 40 percent of the cases (each time independently of what happens in the other cases). However, you don’t know which of the two programs is better
(you could probably figure it out by having them both work on a large number of tasks but that would take very long).

(a) What is the probability that the same program outperforms on both of the next two tasks?
(b) Given that the first program outperformed on the last two tasks, what is the probability that the first program is the better one of the two? (Hint: use the Bayes
formula.)
(c) Given that the first program outperformed on the last two tasks, what is the probability that it will outperform on the next one?