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drfarah · Oct 31, 2009, 09:50 AM

I want to know the answer of this question URGENTLY please:

Q:
State the number of possible outcomes if a fair dice is drown two times. Write down all the possible outcomes that give the following events and calculate then the probability such that:
a)The sum of the two tries is above 5

b) The draws have the same outcome.

Thanks a lot

galactus · Oct 31, 2009, 11:30 AM

There are 36 outcomes. List them out. 1,1; 1,2; 1,3; 1,4; 1,5; 1,6;... and so on.

If there were 3 dice, then there would be 6^3 outcomes. If there were 10 dice, there would be 6^10 outcomes. See the pattern?

There is a quick way to find how many outcomes sum to more than 5.

That means they would have to sum to 6,7,8,9,10,11,12.

It is called a generating function.

$\left(\sum_{k=1}^{6}x^{k}\right)^{2}$

If we expand this we get $x^{2}+2x^{3}+4x^{5}+5x^{6}+6x^{7}+5x^{8}+4x^{9}+3x ^{10}+2x^{11}+x^{12}$

Look at the exponents and their corresponding coefficients(numbers in front of the x's).

Look at the exponents larger than 5 and add up their coefficients. Each number it fron of the x is how many times that sum occurs. For instance, how many ways sum to 7? The coefficient corresponding to x^7 is 6. There are 6 ways the two dice sum to 7. So, the probability we get a sum of 7 is 6/36=1/6.
See? Do this with your case and divide by 36 to fnd the probability. Or, you can list them out and count them up. But I do not like brute force. Especially with counting problems. It defeats the purpose.

drfarah · Nov 1, 2009, 04:01 AM

So the pr(A), where A is the sm of the two tries above 5 = 27/36

and the probability of the second Q is 6/36 (the probabilti of the two of tries are equal)

Thank you very much for your patient and your helpful answers.

Unknown008 · Nov 1, 2009, 05:02 AM

I got 26/36!

I used a probability table.

galactus · Nov 1, 2009, 05:20 AM

Yes, Unknown has it. Just add up the coefficients.

They sum to 26

So, we ave 26/36=13/18

sajidbzu · Nov 1, 2009, 11:40 AM

what is the probability of getting one six if a die is thrown four times?

sajidbzu · Nov 1, 2009, 11:44 AM

if a die is thrown four times what is the probability that the nunber is six?

Unknown008 · Nov 1, 2009, 10:17 PM

Start your own thread sakidbzu. And post the answer you think is good.

drfarah · Nov 2, 2009, 01:22 AM

Oh OK thanks,
And the draws have the same outcome will it be 6/36?

Unknown008 · Nov 2, 2009, 01:31 AM

Yes, exactly! :) Well done!

drfarah · Nov 2, 2009, 12:11 PM

Thank you very much :)

Unknown008 · Nov 2, 2009, 08:26 PM

You're welcome! :)