Truth tellers and liars
speaks the truth 3 out of 4 times, and
5 out of 6 times. What is the probability that they will contradict each other? Give your answer to two decimal places.
Image credit: Jinavie Tumblr .
The answer is 0.33.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Define contradiction to be:
If A tells the truth, B tells a lie If A tells a lie, B tells the truth
Now, to have A and B contradict each other:
A must tell the truth and B must tell a lie OR A must tell a lie and B must tell the truth
P(A tells the truth) = 3/4
P(B tells the truth) = 5/6
P(contradiction) = [P(A tells the truth) x P(B tells a lie)] + [P(A tells a lie) x P(B tells the truth)]
P(contradiction) = [(3/4) x (1/6)] + [(1/4) x (5/6)] = 1/3
And that is the solution.
NOTE: "x" means multiplication