Re: quit gambling, Jim (n/t)

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!!

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:

• Mr S...I have a problem with the solution.. Subhotosh Khan 08:23:14 09/19/02 (3)
  • Re: Mr S...I have a problem with the solution.. Soroban 09:44:40 09/19/02 (2)
    • Mr S...I STILL have a problem with the solution.. Subhotosh Khan 12:27:39 09/19/02 (0)
    • BOTH u and v = 1/sqrt(2) = 0.707106781, right?? Denis Borris 11:02:34 09/19/02 (0)
• Thanks Mr S. I cannot finish it; what is answer? Jim 14:38:37 09/18/02 (5)
  • 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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