Thesus the rat is in a labyrinth. Initially, he is in a chamber with two openings. Thesus always
chooses one of these two possible directions with equal probability.
If he goes right then he needs to walk three minutes only to come back inside to its initial
position.
If he goes to the left, then he needs to walk for one minute before finding a fork in the path. With
probability 1/3 he will choose the upwards path to his right, which leads to the exit, after another
minute walk.
With probability 2/3 he will choose the other way, which after four more minutes walking, will
lead to his departing point. What is the expected time that Theseus will remain in the labyrinth?
Solution
EXPECTED(X) = X1*P(X1)+ X2*P(X2).......+Xn*P(Xn)
probability of right = 1/3
probability of left= 2/3
expected minute = 1*1/3 + 4*2/3 = 9/3 = 3 minute..
Thesus the rat is in a labyrinth. Initially, he is in a chamber with.pdf
1. Thesus the rat is in a labyrinth. Initially, he is in a chamber with two openings. Thesus always
chooses one of these two possible directions with equal probability.
If he goes right then he needs to walk three minutes only to come back inside to its initial
position.
If he goes to the left, then he needs to walk for one minute before finding a fork in the path. With
probability 1/3 he will choose the upwards path to his right, which leads to the exit, after another
minute walk.
With probability 2/3 he will choose the other way, which after four more minutes walking, will
lead to his departing point. What is the expected time that Theseus will remain in the labyrinth?
Solution
EXPECTED(X) = X1*P(X1)+ X2*P(X2).......+Xn*P(Xn)
probability of right = 1/3
probability of left= 2/3
expected minute = 1*1/3 + 4*2/3 = 9/3 = 3 minute.
