Among a group of people, 10% are from NYC and 90% are not. All people from NYC are under 18 years old, and 60% of those not from NYC are also under 18 years old. One person is chosen at random, and he or she is under 18. What is the probability that the person chosen is from NYC? Round your answer to two decimal places.
To find the probability that the person chosen is from NYC, given that they are under 18 years old, we can use conditional probability.
Let's start by finding the probability that a person is under 18 years old. Since 10% of the group is from NYC and we know that all people from NYC are under 18, the probability of selecting a person under 18 is 10%.
Next, we need to find the probability that a person not from NYC is under 18. Since 90% of the group is not from NYC, and 60% of those not from NYC are under 18, we can calculate the probability as follows:
P(Under 18 and not from NYC) = P(Not from NYC) * P(Under 18 | Not from NYC)
= 90% * 60%
= 54%
Now, we can use Bayes' Theorem to find the probability that a person is from NYC given that they are under 18. Bayes' Theorem is given by:
P(NYC | Under 18) = (P(Under 18 | NYC) * P(NYC)) / P(Under 18)
Substituting the values we have:
P(NYC | Under 18) = (100% * 10%) / (10% + 54%)
= 0.10 / 0.64
= 0.15625
Rounding the answer to two decimal places, the probability that the person chosen is from NYC, given that they are under 18 years old, is 0.16.