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Author Topic:   For Inquisitor, et al: What is Evolution?
Percy
Member
Posts: 22479
From: New Hampshire
Joined: 12-23-2000
Member Rating: 4.7


Message 74 of 81 (41021)
05-22-2003 1:07 PM
Reply to: Message 69 by Rrhain
05-21-2003 5:35 PM


Re: An Actual Probability Calculation
Rrhain writes:
Suppose I have n darts, each with a 1/n chance of striking the target. What is the probability of hitting the target at least once given 10 darts? 20 darts? An infinite number of darts? How many darts must you have to be within 99% of the value of an infinite number of darts?
Just noticed this statistics problem for the first time, I'll give it a shot.
Here's the general solution for n, just do the math to find the answers for 10, 20 and darts:
Pn = 1 - (1 - 1/n)n
To find how many darts you must have to be within 99% of the value for darts, simply solve this equation for n:
Pn - P = .01
(1 - (1 - 1/n)n) - (1 - (1 - 1/)) = .01
The term for goes to 0, so this becomes simply:
(1 - (1 - 1/n)n) = .01
That's the answer, but I don't know how to solve the equation.
--Percy

This message is a reply to:
 Message 69 by Rrhain, posted 05-21-2003 5:35 PM Rrhain has replied

Replies to this message:
 Message 77 by Rrhain, posted 05-24-2003 1:23 AM Percy has replied

Percy
Member
Posts: 22479
From: New Hampshire
Joined: 12-23-2000
Member Rating: 4.7


Message 78 of 81 (41233)
05-24-2003 3:36 PM
Reply to: Message 77 by Rrhain
05-24-2003 1:23 AM


Re: An Actual Probability Calculation
Rrhain writes:
quote:
Here's the general solution for n, just do the math to find the answers for 10, 20 and ∞ darts:
Pn = 1 - (1 - 1/n)n
You need to show your work.
This particular part is too elemenary for that, I just wrote it down off the top of my head. I could break it down for you, but why don't we let someone who's figuring it out for the first time do that? This isn't the interesting part of the problem anyway.
Yes, that is the correct formula, but you neglected to say why.
The original hint you provided explains why.
quote:
(1 - (1 - 1/n)n) = .01
That's the answer, but I don't know how to solve the equation.
Incorrect. That is not the answer. The term for does not go to 0.
Oh, you're right! Isn't that interesting. I still don't know how to solve the equation. For example, I don't know how to find log(1-1/n). Just by inspection it looks like n is less than 20, though.
You originally introduced the problem in a reply to Daddy's Message 38 where he was talking about zero chances in a kajilion. Can you tie your probability problem back into the misconception Daddy was experiencing? I think that would be pretty helpful.
--Percy
PS - Your problem showed up a bug in MathCad, which believes the expression for P goes to 0.

This message is a reply to:
 Message 77 by Rrhain, posted 05-24-2003 1:23 AM Rrhain has replied

Replies to this message:
 Message 79 by Rrhain, posted 05-27-2003 5:40 PM Percy has not replied
 Message 80 by Rrhain, posted 05-27-2003 5:50 PM Percy has not replied

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