Probabilities of correct answers

You are lost in the National Park. Tourists (which look just like indians) comprise two-thirds of the visitors to the park, and give a correct answer to requests for directions with probability 3/4. (Answers to repeated questions are independent, even if the question and the person are the same.) If you ask an indian for directions, the answer is always incorrect.

(a) You ask a passerby whether the exit from the Park is East or West. The answer is East.

What is the probability that this is correct?

(2/3)(3/4) + (1/3)(0) = 1/2

(b) You ask the same person again, and receive the same reply. What is the probability of being

correct?

1/2^2 ?

(c) You ask the same person for the third time, and receive the same reply. What is the probability

of being correct?

1/2^3 ?

(d) You ask for the fourth time, and receive the same reply. What is the probability of being

correct?

1/2^4?

(e) Had the fourth answer been West instead, what is the probability of East being correct?

1/2^4 ?

(f) Contrast your answers in part d and part e and explain.

Re: Probabilities of correct answers

(a) fine

(b) p(2 correct answers|indian)*p(indian) + p(2 correct answers|tourist)*p(tourist)

0*1/3 + 0.75^2 = 9/16

(c)

use the same method as (b)

(d)

use the same method as (c)

(e)

This person has given different replies, so must be a tourist. what is the probability of a tourist giving 3 correct answers out of 4?

(f)

should follow from (d) and (e).

Re: Probabilities of correct answers

Quote:

Originally Posted by

**SpringFan25** (a) fine

(b) p(2 correct answers|indian)*p(indian) + p(2 correct answers|tourist)*p(tourist)

0*1/3 + 0.75^2 = 9/16

What happened to the 2/3?

p(2 correct answers|indian)*p(indian) + p(2 correct answers|tourist)*p(tourist)

0*1/3 + (2/3) 0.75^2 ??

Quote:

This person has given different replies, so must be a tourist. what is the probability of a tourist giving 3 correct answers out of 4?

(2/3)(3/4)^3(1/4) ??