Question

The lottery in an extremely small state consists of picking two different numbers from 1 to 10. Ten Ping-Pong balls numbered 1 through 10 are dropped into a fish bowl, and two are selected at random. Suppose you bet on 2 and 9. What is the probability that you won the lottery?

Answer 1

What is the probability of any of the 10 being selected?

Answer 2

1/10

Answer 3

Then the probability of any of the others being selected after that is 1/9 because there is one less to choose from.

Answer 4

There are two ways of getting 2 and 9. 2 then 9 or 9 then 2. Each possibility has a 1/10 x 1/9 chance of happening so each has a 1/90 chance and as there is two possibilities it is 2/90 or 1/45.

Answer 5

That makes better sense, thank you, I was not understanding based on your first two comments

Answer 6

Do you have the answer to this question?? I think, by the question, that the two cards are picked at a time and not one after the other.

Answer 7

Fair enough. Do you get that the probability of taking any ball is 1/10 each?

Answer 8

I think I do, I needed to understand what it was asking. I had two answers and needed to narrow it down but was having a hard time

Answer 9

thank you

Answer 10

The fact that they're taken at the same time is irrelevant. You still have 1/90 chance of picking any combination.

Answer 11

@alrightatmaths may i ask you why you think it's irrelevant? The question has nothing mentioned that the cards are taken one after the other. It just says "two are selected at random". By that, I think that the two cards are taken at the same time. So the probability would be 2/10 = 1/5

Answer 12

No it wouldn't. Each ball has 1/10 to start with, but seeing as you're taking two, the second ball does not have a 1/10 chance of being taken, there is only 9 left to take from.

Answer 13

Even if they are taken at the same time, one is still taken slightly earlier than the other.

Answer 14

And if you'd seen the lottery, you'll see that they are taken one after the other and the fact that the question hasn't clarified that they are means that it isn't important.

Answer 15

Don't take me wrong or offensive, but what you did is completely based on your intuition. I mean you did everything by imagining -- "this would happen this way. let's do it like this". You have to answer the question. How can you say that one card is taken slightly earlier than the other?? Base your answer on what's given.

Answer 16

I have. I believe you're wrong.

Answer 17

I can say that one is taken slightly earlier because no human can take two balls at exactly the same time.

Answer 18

No man! I still don't agree. I can show you how to pick two pin-pong balls at the same time. I don't want this debate to go on because you really aren't getting the point. I respect other's opinions. SO I QUIT.