Random Person Probability Problem

[thechicgeek]

Homework Statement

The probability that a person picked at random is 85 years old is 0.008 . if two people are picked at random find the probability of that:
a. they are both 85
b. neither is 85
c. at least one is 85

I have two questions like this one and I am so confused as to how you would find the answer if you aren't given the pool size. could you show me how one would work this problem out?
Thanks :)

 

[Dick]

You have to try. Start with the first one. Take the pool size to be infinite. So the choice of the first person doesn't affect the probabilities in making the second choice.

 

[chrisk]

A probability of 0.008 means 8 out of a 1000.

 

[thechicgeek]

right so the second result isn't affected by the first result right? You could pick another 85. I'm just trying to understand how they know that the chance of picking an 85 year old is .008 like how do they know that? Am I thinking too hard about this?

 

[thechicgeek]

A probability of 0.008 means 8 out of a 1000.

Hah! okay that makes much more sense. :)

 

[Dick]

Hah! okay that makes much more sense. :)

That doesn't mean the pool size is 1000. I.e. the probability of picking a second 85 year old isn't 7/999. It's still 8/1000.

 

[thechicgeek]

That doesn't mean the pool size is 1000. I.e. the probability of picking a second 85 year old isn't 7/999. It's still 8/1000.

got it. Okay well I'm going to try and work a, b, and c out and see what i can come up with.

 

[thechicgeek]

okay so would a. =.006%
b. =98%
am I on the right track here?

 

[Dick]

okay so would a. =.006%
b. =98%
am I on the right track here?

You multiplied the probabilities, right? I would leave it as 0.000064 rather that changing to % and rounding.
Same with the second. But yes, it looks like you are on the right track.

 

[thechicgeek]

Would c. be .8% or .0079
The professor wants the answer in percentage format.

 

[Dick]

Would c. be .8% or .0079
The professor wants the answer in percentage format.

Ok. Does he want you to round it off too? For c either the first one is 85 and the second one isn't or the second one is 85 and the first one isn't, or they are both 85. You could find the numbers for all three cases and add them. But the simple way to do it is to notice the answer is 1-(probability neither is 85).