[bigchips]

Let's assume the following, and that my hole cards don't contain any of the cards in question. (please check my calculations)

1) After the flop, there is a 3 card flush on the board. What is the probability that one other player holds two flush cards?

1 - (38/47)*(38/46) = 33.2%

2) After the flop there is a pair on the board. What is the probability someone is holding at least Trips?

2/47 + 2/46 = 8.6%

3) After the flop there is a 3 card connected straight on the board (like 5 - 6 - 7). What is the probability that someone is holding a straight?

Under the above assumptions, it is possible to hold a straight by holding any of the following combinations:
8 and 9 or
8 and 4 or
4 and 3

For 8 and 9, & 4 and 3 (the answer seems too high to me):
1 - (43/47) * (42/46) = 16.5% x 2 = 32.9% chance

My own thought is that the answer should really be:
(4/47) * (4/46) = .74% x 2 = 1.5% (but this seems too low)

I'm not sure how to solve for 8 and 4 because some of the numbers are already used in the above equation.

4) After the flop there is no pair on the board. What is the probability that someone flopped two pair? The flop comes (A Q 7)

If someone is holding:
A and Q or
A and 7 or
Q and 7
then they have two pair.

Any corrections / help on any of the above would be greatly welecome.

Thanks,