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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

Respuesta :

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:

[tex]P = P(T)*P(C/T)[/tex]

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:

[tex]P=\frac{2}{3}*\frac{3}{4}=0.5[/tex]

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

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