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

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!!

: Good advice, Dennis!

: 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.)

Follow Ups:

• Have you taken calculus? .... (n/t) Subhotosh Khan 16:02:29 09/18/02 (0)
• Jim: there is a HIGH PROBABILITY that u = v ! Denis Borris 14:57:39 09/18/02 (3)
  • Test Jmiah 14:16:56 10/17/02 (2)
    • Test Jmiah 14:21:12 10/17/02 (1)
      • Re: Test Jmiah 14:25:42 10/17/02 (0)

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