# Proability of drawing an Ace from three separate decks of cards

The problem that I am working on involves three decks of standard playing cards (52 cards, Ace through 2, four suits and two colors).

The question involves finding out the probability of drawing an Ace of any suit from each of the three decks.

The probability for drawing an Ace of any suit from one deck is $4/52$ or $1/13$ which is 0.07692307692 or 7.69%.

What is the formula to work out the probability for drawing an Ace of any suit from each of the three separate decks of cards?

Am I right in thinking that drawing an ace from 3 separate decks is classed as 3 three independent events... so 4/52 x 4/52 x 4/52 = 0.000455166136 ?

• Yes, they are independent because they are 3 different decks and a draw from one deck does not affect the other draws. Your answer is correct, but $\frac{1}{13^3}$ looks prettier. – RandyF May 31 '17 at 18:47

From the first deck, as you said, the probability is $\frac{1}{13}$. This is the probability of drawing an ace from each of the other two decks as well, so the probability of drawing an ace from all three is $$\frac{1}{13}*\frac{1}{13}*\frac{1}{13}$$ $$=\frac{1}{2197}$$