Question

If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?

Answer 1

Refresh my memory: How many blackjacks are there in a standard set of cards?

Answer 2

Also, how many cards are there in a standard set of cards?

Answer 3

Those two questions are essential for solving this problem.

Answer 4

52 cards in a deck

Answer 5

a two card black jack consists of one ace and either (K,Q,J, or 10)

Answer 6

(across is being didactic)

Answer 7

compute the probability that the first is an ace and the second is worth ten given that the first is an ace, the probability that the first is worth ten and the second is an ace given that the first is a ten, then add

Answer 8

if you want to make your life easy do it for one suit and forget about two decks.

Answer 9

so you should get
\[\frac{4}{13}\times \frac{1}{12}+\frac{1}{13}\times \frac{4}{12}=\frac{2}{39}\]

Answer 10

I'm going to do this in multiple posts because I just lost all my work trying to submit.

There are 8 aces and 32 ten-values cards. There are two ways to get a blackjack in two draws: (i) draw an ace then draw a ten or (ii) draw a ten then draw an ace:\[\frac{8}{104}\frac{32}{103}+\frac{32}{104}\frac{8}{103}\]

Answer 11

This is the same as\[=2*\frac{8}{104}\frac{32}{103} = \frac{512}{10712} \approx.0477968633\]

Answer 12

or about 1 in 20.921875 times

Answer 13

you can also use combinations...

\[\frac{{8 \choose 1}{32\choose1}}{{104\choose2}}\]

Answer 14

THANK YOU ALL SO MUCH!!