155k views
3 votes
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

2 Answers

2 votes

Final answer:

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.

User Nagibaba
by
8.1k points
2 votes

Answer:

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

User SMaN
by
9.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories