Among a group of people, 10% are from NYC and 90% are not. All people from NYC are under 18 years old, and 70% 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.

Question

Among a group of people, 10% are from NYC and 90% are not. All people from NYC are under 18 years old, and 70% 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.

i have no idea how to even begin this problem.. please help? :/

Answer 1

To solve this problem, we can use the concept of conditional probability. We need to find the probability that the person chosen is from NYC given that they are under 18 years old.

Let's break down the information given:

1. 10% of the group is from NYC, so the probability of randomly selecting someone from NYC is 10% or 0.10.
2. 90% of the group is not from NYC, so the probability of randomly selecting someone not from NYC is 90% or 0.90.

Now we need to consider the probabilities for the age breakdown:

3. All people from NYC are under 18, which means 100% of them are under 18.
4. 70% of those not from NYC are under 18.

Given that the person chosen is under 18, we can calculate the overall probability of selecting someone from NYC by considering the following steps:

Step 1: Calculate the probability of selecting someone under 18, regardless of their origin:

Probability of being under 18 = (Probability of being from NYC and under 18) + (Probability of not being from NYC and under 18)

Step 2: Calculate the probability of being from NYC, given that the person is under 18:

Probability of being from NYC, given that the person is under 18 = Probability of being from NYC and under 18 / Probability of being under 18

Now, let's calculate the probabilities step by step:

Step 1:
Probability of being under 18 = (Probability of being from NYC and under 18) + (Probability of not being from NYC and under 18)

= (0.10) + (0.90 x 0.70) (as 70% of not being from NYC are under 18)

= 0.10 + 0.63

= 0.73

Step 2:
Probability of being from NYC, given that the person is under 18 = Probability of being from NYC and under 18 / Probability of being under 18

= 0.10 / 0.73

≈ 0.137

So, the probability that the person chosen is from NYC, given that they are under 18 years old, is approximately 0.137 or 13.7%. Round this to two decimal places, the answer is 13.70%.