Question

Assume you are playing with a single standard deck of 52 cards. What is the probability of being dealt Blackjack (exactly 21 in 2 cards)? To get exactly 21, you need one Ace and you need either a 10, Jack, Queen, or King.

Answer 1

first, we need to find the total number of 21 point hands possible

we have 4 aces

we have 4 10's of each color

we have 4 each of Jack, king and queen, so a total of 12 face cards

so, total number of 21 point hands possible = (4 Ace)*(4 10's card + 4 queen + 4 king + 4 Jack) = 4*16

this gives, total number of 21 point hands possible = 64

Number of ways to select 2 cards hand possible in the deck = Combination(52,2) = 52!/[(52-2)!*2!]=1326

so, Required probability = (total number of 21 point hands possible)/(number of ways to select 2 cards)

setting the values, we get

Probability = 64/1326 = 32/663 or 0.0482