Math Forum Discussions

Fakename

Posts: 6
Registered: 9/4/05

Re: coin toss
Posted: Sep 5, 2005 1:34 PM

Plain Text

"Dave Chamberlain" <davec@osmium.mv.net> wrote in message
news:dfgcri$2fls$1@pyrite.mv.net...
>
> Fakename <fakename@comcast.net> wrote:
>
> : If you toss 100 coins, what's the probability of getting 5 (either heads
> or
> : tails in a row)? 6 in a row?
> : How do you figure it out?
>
> If I'm following the question correctly.
>
> Each toss has an equal chance 50/50 (1:2 or 1/2) of being heads or tails.
> If the first toss is heads, the odds of the second toss still has
> a 50/50 chance of being heads.
> Tosses 1 and 2:
> H H
> H T
> T H
> T T
> There are four combinations (2 choices raised to 2 tosses), with
> 2 of them yielding all Heads or Tails. So your chances are
> 2 out of the 4 combinations will be the same. 2/4 = 1/2 = 50%
>
> If you toss the coin a third time:
> H H H
> H H T
> H T H
> H T T
> T H H
> T H T
> T T H
> T T T
> You wind up with 8 combinations, 2 raised to the 3rd power, with
> 2 of those 8 being all the same.
>
> So if you were to toss it 5 times you would have 32 combinations,
> 2^5 (64 combinations if you wanted 6 in a row). With 2 of them
> being all the same.
> With 5 coins: 2:32 = 1:16 = 6.25%
> With 6 coins: 2:64 = 1:32 = 3.125%
>
>

No, what I mean is ...if you tossed the coin exactly 100 times, what is the
probability that you will get at least one run of five in a row (either
heads or tails)?
> --
>
> -davec
> -----------------------------------------------------------------
>

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