Suppose you repeatedly play hands of Texas HoldSolutiona Y

Suppose you repeatedly play hands of Texas Hold

Solution

a) Y = min{X1,X2}

Let p = P(get pair or 2 black cards) = 13*C(4,2)/C(52,2) + C(26,2)/C(52,2) - 13/C(52,2) = 29.41%.

q = 1-p = 70.59%. Y is geometric with p = 29.41%, so P(Y=k) = q^k-1 p

=0 .7059^k-1 * 0.2941.

b) Z = max{X1,X2}

P(Z > k) = P(X1 > k or X2 > k) = P(X1 > k) + P(X2 > k) - P(X1 > k and X2 > k).

Let p1 = P(dealt a pocket pair) = 13*C(4,2)/C(52,2) = 5.88%. q1 = 1-p1 = 94.12%.

p2 = P(dealt two black cards) = C(26,2)/C(52,2) = 24.5%. q2 = 1-p2 = 75.5%.

P(Z > k) = q1^k + q2^k