You are lost in the national park of Bandrika Tourists compr

You are lost in the national park of Bandrika. Tourists comprise 2/3 of the visitors to the park and give the correct answer to requests for directions with probability 3/4. If you ask a native badrikan for directions the answer is always false.

(A) You ask a passer-by for directions to the exit. What is the probability that the directions are correct?

(B) Calculate the probability that the passer-by was a tourist given that the directions were correct.

(C) It turns out the directions are NOT correct. Calculate teh probability that the passer-by was a tourist.

Solution

A.) P(Directions correct) = (2/3)*(3/4) + (1/3)*(0) = 1/2 = 0.5

B.) P(Tourist|Directions correct) = (2/3)*(3/4)/P(Directions correct) = 0.5/0.5 = 1

C.) P(Directions not correct) = 1 - P(Directions correct) = 1 - 0.5 = 0.5

P(tourist|Directions not correct) = (2/3)*(1/4)/P(Directions not correct) = (1/6)/0.5 = 1/3