We will find that the probability that exactly one is original (or that exactly two are fakes) is 0.038
We know that 12% of the paintings are replicas.
Then if we see a random painting, the probability that it is a replica is 0.12
This means that the probability that a random painting is not a replica, is 1 - 0.12 = 0.88
Now we want to find the probability that exactly two out of 3 paintings are fake.
An easier thing to find is the probability that exactly one of the paintings is original (is exactly the same thing, just another viewpoint).
Let's assume the paintings are ordered, and the first one is the original one.
The probability of this will be:
P = 0.88*0.12*0.12
But we also have the case where the second one is the original, and the case where the third one is the original, so we have 3 possible permutations.
This means that the probability that exactly one is original (or that exactly two are fakes) is:
P = 3*(0.88*0.12*0.12) = 0.038
If you want to learn more, you can read:
https://brainly.com/question/9793303
