Answer:
The probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).
Step-by-step explanation:
We have here a case where we need to use Bayes' Theorem and all conditional probabilities related. Roughly speaking, a conditional probability is a kind of probability where an event determines the occurrence of another event. Mathematically:
In the case of the Bayes' Theorem, we have also a conditional probability where one event is the sum of different probabilities.
We have a series of different probabilities that we have to distinguish one from the others:
The probability that a person has a tattoo assuming that is a Millennial is:
The probability that a person has a tattoo assuming that is of Generation X is:
The probability that a person has a tattoo assuming that is of Boomers is:
The probability of being of Millennials is:
The probability of being of Generation X is:
The probability of being of Boomers is:
Therefore, the probability of the event of having a tattoo P(T) is:
For non-independent events that happen at the same time, we can say that the probability of occurring simultaneously is:
Or
But
Then
We are asked for the probability that a person is a Millennial given or assuming that they have tattoos or P(M | T). Solving the previous formula for the latter:
We have already know that
.
Therefore
Thus, the probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).
