SOLUTION: Suppose that you select 3 cards without replacement from a standard deck of 52 playing cards. a) If the first card that you select is a king and the second is a two, what is th

Then you have a deck of 50 cards, with only three twos and three kings.

3 kings out of 50 = 

You can look at this an easy way or a hard way.  

Easy way:  Since you don't know what the suit of the first card was, it's
no more or less likely that the second card will be one suit than that it 
will be any other suit,  so the probability is just  that it will
be a spade.
 
Hard way:  If the 4 is a spade there are 12 spades among the 51,
but if the 4 is not a spade, there are 13 spades among the 51. 

P(spade second) = 

P[(the 4 is a spade AND spade 2nd) OR (the 4 is not a spade AND spade 2nd) 

Remember that "AND" implies "multiplication" and "OR" implies "ADDITION":

P(the 4 is a spade)*P(spade 2nd in that case) + P(the 4 is not a spade)*P(spade 2nd in that case)

 



That's harder, but it demonstrates that the easy way is correct.

Edwin