Card Probability

Question

probability of drawing a spade and then a red card from a standard deck of cards WITHOUT replacement

Answer 1

Without replacement, you need to consider that your deck is getting smaller. A standard deck is 52 cards.

1/4 of cards in the deck are spades, so this will be your probability for drawing a spade first. After drawing this card, there are only 51 in the deck.

Spades are black, so there's one more red card in the deck than black. The probability now of drawing a red card is 26/51.

The probability of drawing a spade and then a red card without replacement will be 1/4 * 26/51, or 13/102.