# Re: quit gambling, Jim (n/t)

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Posted by Soroban on September 18, 2002 at 13:33:52:

In Reply to: quit gambling, Jim (n/t) posted by Denis Borris on September 18, 2002 at 02:41:54:

: : You are given two coins and toss each one once.
: : The probability of getting a head on the first
: : coin is u and the probability of getting a head
: : on the second coin is v where u<=v.

: : The probability of getting 2 heads is 1/2.
: : The probability of getting 2 tails is at a maximum
: : subject to that condition.

: : Calculate u,v each to 4 decimal places.

: : HELP!!

Jim,
This is an interesting max/min problem.

Probability of two heads is 1/2:
P(HH) = P(H1)*P(H2) = u*v = 1/2, or v = 1/2u

Probability of two tails is to be maximized:
P(TT) = P(T1)*P(T2) = (1 - u)(1 - v)

There is the function we are to maximize!
P = (1 - u)(1 - v)

Since v = 1/2u: P = (1 - u)(1 - 1/2u)

You can finish it from here, right?
(Differentiate, set equal to zero, solve, etc.)

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