# Thread: Probabilty black jack

1. ## Probabilty black jack

Having trouble intepreting this question. could someone help me interpret it.

In the game of blackjack, you are initially dealt two cards from a standard deck of cards. If they have the same value, for example two 3s or two jacks, you can 'split them', making each one the first card of two seperate games.

a)find probability that you are dealt 2 cards of the same value that can be split

-with this should i design a table that displays a vertical and horizontal axis with cards Ace-King, just as you would do if two dice were rolled? and then figure out the probability of cards of the same value?

b) in 800 games of blackjack, about how many times are such a pair dealt?

If anyone could help, that would be great thanks.

b) in 800 games of black jack, about how many times

2. ## Re: Probabilty black jack

b) is a binomial, the expected number is np, where n=800 and p is obtained in (a)

For (a), there is other information that is missing, such as other people's top cards and how many players.
BUT if you just want to know the chance of a pairs it would be 3/51.
The first card can be anything and the chance you have a match on the second would be 3/51=1/17.
OR use the hypergeometric....

$\displaystyle {13{4\choose 2}{48\choose 0}\over {52\choose 2}}$

3. ## Re: Probabilty black jack

Hello, johnsy123!

In the game of blackjack, you are initially dealt two cards from a standard deck of cards.
If they have the same value, for example two 3s or two jacks, you can 'split them',
making each one the first card of two seperate games.

a) Find probability that you are dealt 2 cards of the same value that can be split.

The first card can be any card: .$\displaystyle \frac{52}{52}$
The second card must match the value of the first card: .$\displaystyle \frac{3}{51}$
Therefore: .$\displaystyle P(\text{pair}) \:=\:\frac{52}{52}\cdot\frac{3}{51} \:=\:\frac{1}{17}$

b) in 800 games of blackjack, about how many times are such a pair dealt?

$\displaystyle \frac{1}{17}\times 800 \:=\:47.0588\hdots$

About 47 times.