Q:

Card pair probability

I have a small pyramid of cards on the table (two cards face down at the bottom, one card face down at the top). 
What is the probability of first selecting a red card in the remaining deck of 49, then flipping over one of the lower-level pyramid cards followed by the upper-level pyramid card and hoping that both of these two cards are pairs? 

A:

Hint: The pyramid doesn't matter at all, just think of drawing three cards in order.   The chance of getting a red card first is $\frac 12$.  If by "these two cards are pairs" you mean the second and third are to match in rank you need to distinguish the cases where the second card matches the first and where it does not.   What is the chance the second card matches the first?   Given that the first two match, what is the chance that the third matches them?   Multiply all these together to get the chance you drew three of a kind.   Then, start again with the $\frac 12$, what is the chance that the second card doesn't match the first?   Given that they do not match, what is the chance the third card matches the second?   Again, multiply these together, then add the products (they are exclusive possibilities) and you are home. 
Added:  roughly, it is $\frac 12$ for the color and $\frac 1{13}$ for the two cards to match, for a product of $\frac 1{26}$.  More exactly, $\frac 12(\frac 3{51}\cdot \frac 2{50}+\frac {48}{51}\cdot \frac 3{50})=\frac 1{34}$.  The reduction comes because we have removed one of the cards that could be a pair on the second draw.