Probability of the dealer having the same up card in BJ

Hi BruceZ,

The formula you show:

sum[k=7,10]C(10,k)*(1/52)^k*(51/52)^(10-k) = 1.1 x 10^-10
= 1 in 9 billion (American billion).

Includes the probability for the same BJ predetermined card being the upcard for 7 out of 10 deals + 8 out of 10 deals + 9 out of 10 deals + 10 out of 10 deals. No big deal -- but did not the problem definition only ask for the chance of the same upcard coming up exactly 7 times out of 10. Your formula is for 7 or more. The problem definition should have said for 7 or more repeats for a sample of 10 deals.

Actually Bruce, I appreciate your expertise and learned a lot from your reply on this and other probability things. Thanks for your effort.