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
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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
(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?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
