Anonymous

# there are three cards in a hat; one king, one queen, and one ace?

there are 3 cards in a hat; one is a king, a queen, and one is an ace. two cards are to be selected at random without replacement. what is the sample space? and what is the probability that you choose the same card twice?

Relevance

The question says without replacement, so you would not put the card back:

Therefore, the probability that you would draw the same card twice (since you don't put it back into the hat... without replacement, no replacing) would be Zero.

Oh, and the sample space would be:

{KQ, KA, AQ}

• Anonymous

I don't know about sample space, but when you find probabilities, you multiply fractions.

You've got a 1/3 chance of picking a certain card. After you do, you put it back. What's the chance you pick that card? 1/3, again.

For those two times in a row, you multiply a third by a third.

If you mark first card you choose with x, and the second by y, and the cards with 1,2,3, your simple space would be

{(x,y) | x,y:1,2,3}

So only one choise suits you, when x=y, (1,1),(2,2),(3,3).

The probability is 3/9=1/3, since x could be any of three cards, and y could be any of three cards.

Edit: if you do not put the card back probability would indeed be 0.