# Jim: there is a HIGH PROBABILITY that u = v !

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Posted by Denis Borris on September 18, 2002 at 14:57:39:

In Reply to: Thanks Mr S. I cannot finish it; what is answer? posted by Jim on September 18, 2002 at 14:38:37:

: : : : 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.)

• Test Jmiah 14:16:56 10/17/02 (2)
• Test Jmiah 14:21:12 10/17/02 (1)

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