# Thanks Mr S. I cannot finish it; what is answer?

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Posted by Jim on September 18, 2002 at 14:38:37:

In Reply to: Re: quit gambling, Jim (n/t) posted by Soroban on September 18, 2002 at 13:33:52:

: : : 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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