Question

You draw 2 cards from a well-shuffled deck of 52 cards. after you draw the first card, you do not replace it in the deck. What is the probability of P(get ace of spades on first draw and get queen of hearts of second draw)?

Answer 1

Lets look at the first draw of the first card. There are 52 cards. There is only one Ace of Spades. So the chances of drawing the Ace of Spades on the first draw is:
\[\frac{ 1 }{ 52 }\]Now, for the second draw, there is only one Queen of Hearts, but there are now only 51 cards, so the chance of drawing the Queen of Hearts is:
\[\frac{ 1 }{ 51 }\]The chances of both happening is the product of these probabilities:
\[\frac{ 1 }{ 51 \times 52 }\]