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## Difficult Math Problem #108 - Probability

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800guy Master | Next Rank: 500 Posts
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#### Difficult Math Problem #108 - Probability

Mon Mar 12, 2007 12:02 pm
A and B alternately toss a coin. The first one to turn up a head wins. if no more than five tosses each are allowed for a single game.

1- Find the probability that the person who tosses first will win the game?

2- What are the odds against A's losing if she goes first?

oa coming when people respond with explanations. from diff math doc

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800guy Master | Next Rank: 500 Posts
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Wed Mar 14, 2007 8:41 am
agreed, this is really tough

800guy Master | Next Rank: 500 Posts
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Wed Mar 14, 2007 8:41 am
here's the oa from the doc:

look at the conditions; it says that the first person who tosses a head wins.

Let's say A tosses first.

what is the probability that he wins

H + TTH + TTTTH + TTTTTTH + TTTTTTTTH

i.e. either the first toss is head,
or the first time A tosses the coin he gets a tail and B also gets a tail , n in the second throw A gets a head.....

This continues for a max till 5 throws, because the game is for 5 throws only.
So, 1. 1/2 + (1/2)^3 + (1/2)^5 + (1/2)^7 + (1/2)^9

2. (1/2)^2 + (1/2)^4 + (1/2)^6 + (1/2)^8 + (1/2)^10

800guy Master | Next Rank: 500 Posts
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Wed Mar 14, 2007 8:41 am
agreed, this is really tough

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