# Thread: Probability: Is it conditional?

1. ## Probability: Is it conditional?

I'm having trouble telling if this is meant to be conditional probability or not.

A chart showing results from a survey of adults regarding tattoos is shown below. Assuming the data are representative, estimate the probabilities that:
a) A randomly selected person has a tattoo, and
b) A randomly selected person of age between 18 and 29 has a tattoo.

Data:
At least one tattoo:
Age 18-29: 18
Age 30-50: 6

No tattoo:
Age 18-29: 32
Age 30-50: 44

For part a, I simply did the probability that someone would have a tattoo (any age). 18+6 = 24, or 24% probability that someone would have a tattoo. I think that's correct.

Part b is where I start to get a little confused. I thought I might need to use conditional probability, P(age 18-29 | at least one tattoo), which would be 18/24=75%. Then I started to question it, and wondered if it was maybe P(at least one tattoo | age 18-29), which would be 18/50=36%.

...now I'm wondering if the answer isn't just 18% (because 18 out of 100 people will be 18-29 and have one tattoo). I suppose that could be right, since the question never states "given that," which would signify conditional probability. Any help is greatly appreciated.

2. Originally Posted by jacobaf20
I'm having trouble telling if this is meant to be conditional probability or not.

A chart showing results from a survey of adults regarding tattoos is shown below. Assuming the data are representative, estimate the probabilities that:
a) A randomly selected person has a tattoo, and
b) A randomly selected person of age between 18 and 29 has a tattoo.

Data:
At least one tattoo:
Age 18-29: 18
Age 30-50: 6

No tattoo:
Age 18-29: 32
Age 30-50: 44

For part a, I simply did the probability that someone would have a tattoo (any age). 18+6 = 24, or 24% probability that someone would have a tattoo. I think that's correct.

Part b is where I start to get a little confused. I thought I might need to use conditional probability, P(age 18-29 | at least one tattoo), which would be 18/24=75%. Then I started to question it, and wondered if it was maybe P(at least one tattoo | age 18-29), which would be 18/50=36%.

...now I'm wondering if the answer isn't just 18% (because 18 out of 100 people will be 18-29 and have one tattoo). I suppose that could be right, since the question never states "given that," which would signify conditional probability. Any help is greatly appreciated.

You should be more confidence.
The question (b) has give you a condition that "person of age between 18 and 29", that means you should only looking at the person of age between 18 and 29. Therefore the answer is 36%.