Question

In: Statistics and Probability

The probability that one has been to Antarctica given that one is a traveler is .05....

The probability that one has been to Antarctica given that one is a traveler is .05. The probability that one has not been to Antarctica given that one is not a traveler is .999. The probability that one is a traveler is .10.

a/ What is the probability of having been to Antarctica?

b/ What is the probability of not being a traveler, given that you have been to Antarctica?

Expert Solution

Let,

A: event that one has been to Antarctica.

T: event that one is a traveler.

We have given,

Probability that one is a traveler, P(T) = 0.10

Probability that one has been to Antarctica given that one is a traveler, P(A | T) = 0.05

Probability that one has not been to Antarctica given that one is not a traveler, P(Ac| Tc) = 0.999

So,

Probability that one has been to Antarctica given that one is not a traveler, P(A | Tc) = 1- 0.999 = 0.001

Probability that one is not a traveler, P(Tc) = 1- 0.10 = 0.90

Now,

a) The probability of having been to Antarctica = P(A | T) + P(A | Tc)

= 0.05 +0.001

= 0.051

b) The probability of not being a traveler, given that you have been to Antarctica i.e. P(Tc| A)

Using bayes theorem, we have

orchestra answered 1 year ago

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