remaining: 2 Two cards are drawn without replacement from a standard deck of 52 52 playing cards. What is the probability of choosing a heart and then, without replacement, a spade?

Answer 1

The probability of choosing a heart, P(Heart) = 13/52 = 0.25.

Without replacement, you now have 51 cards left in the deck.

So the probability of subsequently choosing a Spade is, P(Spade) = 13/51.

The probability of choosing a heart AND then a space, without replacement is:

(13/52) * (13/51) = .06372549

(Remember, "AND" statements envoke the multiplication rule; "OR" statements envoke the additional rule. And when you sample WITH replacement, you have to then account for the missing cards in subsequent draws.)

I hope this helps.

James

Answer 2

Each deck of 52 cards has 13 hearts, 13 clubs, 13 spades and 13 diamonds.

For the first draw, the probability of a heart is 13/52 = 1/4 = 0.2500.

The card is not replaced, so 51 cards remain in the deck.

For the second draw, the probability of a spade is 13/51 = 0.2549.

Thus the probability of drawing a heart then a spade, without repacement, is 13/52*13/51 = 0.2500*0.2549 = 0.0637