Posted by Subhotosh Khan on September 18, 2002 at 16:02:29:
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!!
: : 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.)