# 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?

### 4 Answers

- 1 decade agoFavorite Answer
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}

- Anonymous1 decade ago
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.

- 1 decade ago
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.

- rothenburgerLv 43 years ago
you're continually unfastened to examine different guides at the same time as interpreting the Bible instruct e book. while i became not yet baptized, the literature we use in our learn is the brochure "What Does God Require individuals." i come across it much less annoying than the Bible instruct e book given this is concise. decrease back then, I kinda experience an identical way you experience, desirous to be responsive to greater and learn deeper issues. So what I deed, at the same time as i'm being studied on the brochure, I even have my very own in my opinion learn using different literatures which i come across greater deeper than the literature the place i'm being studied. usually i attempt to examine old literatures or old bible learn aids utilized by using Jehovah's Witnesses like the e book "you may stay invariably on Paradise on earth," "Daniel's Prophecy," before i became baptized I already finished reading those books. It helped me a lot, decrease back then I raised many questions and as solutions are given i became waiting to comprehend some deeper teachings besides the reality that i became nevertheless a bible learn that component. you're able to do an identical, at the same time as being studied on the Bible instruct, you have your guy or woman very own learn from different literatures that are deeper than the Bible instruct. good day!