# Thread: What does this mean??

1. ## What does this mean??

An article discussing recidivism of juvenile prisoners between 14 and 17 years olld, indicating that 82% of those released were rearrested within 3 years. Solve the following problem for six newly released juvenile prisoners between 14 and 17.

a. Determine the probability that the number rearrested within 3 years will be exactly four; at least four; at most five; between two and five; inclusive.

I know how to figure out this problem, but I have a question. When I am trying to figure the probability of 0 being rearrested I use the formula

P(X=0) (6 0) 6!/0!(6-0)! (.82)^0(.18)^6

which I figure to be 1(.82)(.18)^6 my problem is, on my calculator it says 2.789002368E-5 what does this number mean? I get a similar answer with an E when figuring probability for 1.

2. E^-5 = 10^-5
This is not the exponential function.

3. I'm still confused

4. You got the value on your calculator to be $\displaystyle 2.789002368\text{E}-5$. What it actually means:

$\displaystyle 2.789002368\text{E}-5 = 2.789002368 \cdot 10^{-5}$

5. So, how do I change that into percent form for the probability?

6. I'm not sure, sorry. I think this is preset into the calculator itself. Maybe you can change it to show decimals only, but I'm not sure. I'll let someone who knows much 'bout calculators take over

7. Originally Posted by sjenkins
An article discussing recidivism of juvenile prisoners between 14 and 17 years olld, indicating that 82% of those released were rearrested within 3 years. Solve the following problem for six newly released juvenile prisoners between 14 and 17.

a. Determine the probability that the number rearrested within 3 years will be exactly four; at least four; at most five; between two and five; inclusive.

I know how to figure out this problem, but I have a question. When I am trying to figure the probability of 0 being rearrested I use the formula

P(X=0) (6 0) 6!/0!(6-0)! (.82)^0(.18)^6

which I figure to be 1(.82)(.18)^6 my problem is, on my calculator it says 2.789002368E-5 what does this number mean? I get a similar answer with an E when figuring probability for 1.
The "E" is used by the calculator when answers are really small. This is the calculator's way of using scientific notation. 2.789002368E-5 is the same thing as $\displaystyle 2.789002368\times 10^{-5}$, as Chop Suey had mentioned. In decimal form, this would be the equivalent of $\displaystyle .00002789002368$

If you were interpret this value [in terms of the likeliness of an event], this would be a very unlikely thing that would occur [I'm saying this with a little knowledge about probabilty...I'm no expert. However, I think I said this correctly].

I hope this clarify things.

--Chris

EDIT: In percent form, this would be .002789002368%.

8. Originally Posted by sjenkins
So, how do I change that into percent form for the probability?
To convert any number into a percentage you multiply by 100.

9. I do know how to change a number to a percent, but I was just confused with this particular number.

Thanks for the help though!