A tattoo enthusiast website claims that :

• 47% of Millennials have tattoos
• 36% of Generation X have tattoos
• 13% of Boomers have tattoos

whereas the population proportions are 22%, 20%, and 22% for those generations respectively.?

Compute the probability that a person is a Millennial given that they have tattoos.

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%).

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step-by-step explanation: