Задача с экзамена по Quantitative Methods in Economics. Задача на английском языке. A rogue elf has leaked this year's Santa Claus' list containing the behaviour of kids in three countries A,B and C. The list categorizes children's behaviour as "nice" or "naughty". Of all the kids on the list 35% belong to country A, 40% to country B and the rest to country C. Also, 40% of kids from country A , 25% from country B and 20% from country C , respectively, are listed as "naughty". Given that kid is listed as "nice" in the leaked Santa's list, what is probability that such a kid is from country C?

Предыдущий
вопрос Следующий
вопрос

To solve this problem, we can use Bayes' Theorem.

Let:

A be the event that a kid is from country AB be the event that a kid is from country BC be the event that a kid is from country CN be the event that a kid is listed as "naughty"T be the event that a kid is listed as "nice"

We are asked to find the probability that a kid is from country C, given that the kid is listed as "nice", which is P(C|T).

According to Bayes' Theorem, we have:

P(C|T) = P(C and T) / P(T)

We can calculate P(C and T) as follows:

P(C and T) = P(C) P(T|C)
= 0.25 0.2
= 0.05

Now, we can calculate P(T) as:

P(T) = P(A and T) + P(B and T) + P(C and T)
= P(A) P(T|A) + P(B) P(T|B) + P(C) P(T|C)
= 0.35 0.6 + 0.4 0.75 + 0.25 0.8
= 0.21 + 0.3 + 0.2
= 0.71

Finally, we can now find P(C|T) using Bayes' Theorem:

P(C|T) = P(C and T) / P(T)
= 0.05 / 0.71
≈ 0.07

Therefore, the probability that a kid listed as "nice" is from country C is approximately 0.07.