semi crosspost penny problem

[Don West]

[ QUOTE ]
"There are 10 pennies in a jar. 9 of them are regular pennies, but the tenth penny is a fake coin with heads on both sides. You grab a penny at random and flip it 5 times. All 5 times it comes up heads. How likely is it that it was the 2 headed penny?"

[/ QUOTE ]

this was posed in the finance and investing forum but no answer was given, below is my (likely incorrect) solution.

i'm getting 87.2%
1 - (.9/32 + .1)

poor logic i'd assume. i feel so much dumber than like 5-6 years ago.

anyone care to enlighten me? this is driving me crazy. <font color="white"> </font>

[rufus]

(Edited because I can't count on my fingers)
Let's assume that you draw a penny with equal probability.
Let's assume that all of the other pennies are fair.

Then we have the following scenarios that could have led to your result:
9/10 a fair penny is chosen * 1/32 you get 5 heads with a fair penny:
9/320
and
1/10 you choose the fixed penny * 1/1 you get 5 heads with the fixed penny:
1/10=32/320

So, the chance that it occured is 41/640 and the chance that it happened with the 2-headed penny is 32/320 so the chance that it was the bad penny is:
(32/320)/(41/320)=32/41

That's roughly 78.0%

(
Or if you prefer the math looks like:
.1/(.9/32 + .1)
)

[Don West]

[ QUOTE ]
1/64 you get 5 heads with a fair penny


[/ QUOTE ]

2^5=32 shouldn't this be 1/32?

[rufus]

(putting on my dunce cap)
Yep so the answer I gave is wrong, but you should have little trouble applying the math.

[SumZero]

[ QUOTE ]
[ QUOTE ]
1/64 you get 5 heads with a fair penny


[/ QUOTE ]

2^5=32 shouldn't this be 1/32?

[/ QUOTE ]

Depends on your language. For some of us 2^5 == 7.