Question

You are lost on Mythy Island in the summer, when tourists are 2/3 of the population. If you ask a tourist for directions the answer is correct with probability 3/4, answers to repeated questions are independent even if the question is the same. If you ask a local for directs, the answer is always false. (a). (5 pts) You ask a random passer-by whether Mythy City is East or West. The answer you receive is East. What is the probability that it is correct

Answer 1

To find the probability that the answer you received is correct, you need to use conditional probability. Let's define the events: A: The answer received is East, B: The answer is correct. The probability that the answer is correct, given that it is East, is 1/2.

Step-by-step explanation:

To find the probability that the answer you received is correct, you need to use conditional probability. Let's define the events:

• A: The answer received is East
• B: The answer is correct

The probability of event A is the probability that a tourist responds East, which is 2/3. The probability of event B is the probability that a tourist responds correctly, given that they answered East, which is 3/4.

Now, we can use the formula for conditional probability to find the probability that the answer is correct, given that it is East:

P(B|A) = P(A ∩ B) / P(A)

Substituting the given probabilities, we get:

P(B|A) = (2/3) * (3/4) / (2/3) = 1/2

Therefore, the probability that the answer is correct, given that it is East, is 1/2.

Answer 2

P = 0.5

Step-by-step explanation:

Let's call T the event that you ask a tourist for directions and C the event that you receive a correct answer.

So, we need to find the probability that the random passer-by give you a correct answer. This probability is equal to:

`P = P(T)*P(C/T)`

Where P(T) is the probability that you ask a tourist and P(C/T) is the probability that the tourist give you a correct answer.

We don't take into account the possibility that you ask a local because the answer of a local is always false or incorrect.

Therefore, replacing P(T) by 2/3 and P(C/T) by 3/4, we get:

`P=(2)/(3)*(3)/(4)=0.5`

It means that the probability that the random passer-by give you a correct answer is equal to 0.5