Four cards are dealt at random from a standard what is the likelihood that two are black and two are red

There is a 5/16 chance that you have exactly 2 red and 2 black cards.

To start, there are 16 possibilities. 2^4 = 16.

Now, we just need to determine the total number of black cards in each hand. It follows pascal's triangle.

Black  Number
0       1
1       4
2       6
3       4
4       1

Looking at the table, we see that there are 6 ways out of the 16 ways to have 2 black cards, thus also having 2 red cards.