Please help me figure this out

I was wondering if this makes sense:

If 45/1000 people commit violent crimes each year... could I multiply that by the average life expectancy and get the chance of each person committing a violent crime in their life time? If not, is there anyway to get that figure from the 45/1000 number?

Thanks for your help!~

Re: Please help me figure this out

HeyBigManOnCampus.

Are the probabilities independent for each year? (Hint: Consider P(Commit Year 1 OR Commit Year 2 OR .... OR Commit Year N)).

Re: Please help me figure this out

Hello, BMOC!

Quote:

I was wondering if this makes sense:

If 45/1000 people commit violent crimes each year, could I multiply that by the average life expectancy

and get the chance of each person committing a violent crime in their life time?

If not, is there anyway to get that figure from the 45/1000 number?

No, your method does not make sense.

You say 4.5% of the people commit a violent crime each year.

Then someone who is 23 years old has a probability of:

. . $\displaystyle 23 \times 4.5\% \,=\,103.5\%$ of committing a violent crime at some time.

The set up is not realistic.

Say, 1000 people (including you) draw numbers from a hat

. . and a certain 45 of them must commit a violent crime.

The probability that you do *not* commit a crime that year is 95.5%.

Suppose you enter this "lottery" every year.

How likely are you commit a crime?

The probability that you do *not* commit a crime for 35 years

. . is:.$\displaystyle (0.955)^{30} \:=\:0.199580454 \:\approx\:20\%$

Therefore, the probability that you *do* commit a violent crime

. . at least once during your first 35 years is $\displaystyle 80\%.$

*Ha!*