Alex and Mary take turns tossing one die; Alex goes first. The winner is the first player to throw a 4. Find a number for the probability that Alex wins.
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P[throw 4] = 1/6 = p, P[throw non-4] = 5/6 = q
P[A wins] = p + q^2 *p + q^4*p + .........
which is a G.P. with a = p, r = q^2
sum to infinity = a/(1-r) = p/(1-q^2) = [1/6]/[ 1 - (5/6)^2 ] = 36/66 = 6/11 <------
P[A wins] = p + q^2 *p + q^4*p + .........
which is a G.P. with a = p, r = q^2
sum to infinity = a/(1-r) = p/(1-q^2) = [1/6]/[ 1 - (5/6)^2 ] = 36/66 = 6/11 <------