I'm trying to learn probability and statistics but I can't really get my head around this one. I realize after drawing the first card there will only be 51 cards in the deck but I'm having trouble calculating the chance that the second one is an Ace if I don't know what the first card is?
Assuming that the initial card was an Ace, I could say the probability of the second being an Ace is 3/51… but how do I approach this with an unknown card?
Best Answer
There are $52\times 51$ outcomes when you draw 2 cards one after another without returning the first drawn card to the deck.
There are $48\times 4$ outcomes when the first card is not Ace and the second card is Ace. There are $4\times 3$ outcomes when both cards are Ace. The total outcomes are $48\times 4 + 4 \times 3 = 51\times 4$.
The probability is $\frac{51\times 4}{52\times 51}=\frac{51}{52}\times\frac{4}{51}=\frac{4}{52}=\frac{1}{13}$.