Question

Two cards are randomly selected from an ordinary playing deck. What is the probability that they form a blackjack? That is, what is the probability that one of the cards is an ace and the other one is either a ten, a jack, a queen, or a king?

Answer 1

0.0483 or 4.83%

Explanation:

Assuming that the order at which the cards are drawn is not important. There are 4 cards of each kind in a deck, that is, 4 aces and (4+4+4+4) kings, queens, jacks and tens.

The total number of ways to get a blackjack is:

`N = 4*(4+4+4+4) =64`

The total number of ways to pick 2 cards out of 52 is:

`n = (52!)/((52-2)!*2!)\\ n=1,326`

The probability of getting a blackjack is:

`P = (N)/(n)=(64)/(1,326) = 0.0483`