I'm trying to figure out a math problem, and hope somebody can help me
answer it.  Here goes:
If I roll a pair of dice 24 times, what is the probability that I will
roll a pair of sixes at least once?

I know that you have a 1 in 36 chance of rolling a pair of sixes on
any given roll, but how do I find the probability that I will roll at
least one pair of sixes out of 24 rolls?

---

Clarification of Question by syberkhanx-ga on 01 Feb 2005 20:09 PST

Many thanks to the both of you - Now I just need to know what to do
for this post to have an "answer" and not acomment...   or is that
only for certain moderators?  thanks again,
~SyberKhanX

1- (35/36)**24

 35/36  probability that a double six will NOT show when 1 dice is rolled
 (35/36)**24 probability that double six will never show when dice is rolled 
 24 times.
 1- (35/36)**24 probability that double six will appear at least once.

Mongolia

Mongolia's answer is correct. In case you're not sure, the ** stands
for "raised to the power of", so the answer is 1 - (35/36)^24 = 0.491,
roughly about 50%. In other words, there is roughly about 50% chance
that you will roll at least one pair of sixes out of 24 rolls.

pkuanko
many thanks for actually evaluating my expression. 
I tried to use microsoft's bogstandard calculator.
However as it does not have a 'power to' I got
lazy and gave up. I have though since used Google's
calculator which is actually pretty cool. (it even 
allows you to do calculations with complex numbers
Boy I was impressed!!)

Merci

Mongolia

hi syberkhanx
As pkuanko and myself are not Google researchers we cannot actually 'formally'
answer your question as an actual researcher can. As our comments have
I believe answered your question then I expect no researcher will
attempt to
'answer' your question. Since non reserchers do not get paid this
should be a freebie.

As someone who uses this service from time to time , sometimes non
researchers will provide the answer. Both researchers and
non-researchers can provide
comments (researcher names are coloured  blue and non researchers are
coloured black.

You may wish to look up question 232837 as a good example of a non-researcher 
coming up with the correct answer.

Many Thanks

Mongolia

To Syberkhanx:
You don't have to do anything. Just let the question expire and you
save 5 bucks. I don't think any researcher worth his salt would post
an answer after the correct answer has been given in the comments.

To Mongolia:
You may wish to look up question 466945 as a good example of a
researcher coming up with an incorrect answer!

To Mongolia:
Sorry, the incorrect solution in 466945 didn't come from a reseacher.
I thought it did, because after his solution, he asked "Do you accept
this as an answer?" and I thought he was going to post his incorrect
solution as the answer.

Best regards,
pkuanko

Note that Microsoft's calculator *does* provide a power key, you just
have to switch to the Scientific view. It also has lots of other nice
buttons. I use it as my main calculator (after the one in my head). I
actually tend to forget that by default it doesn't have all the
interesting bits.

dear manuka

you are absolutely right. I just brought up the scientific version and its
pretty good.

Well you do soemtimes learn something new.

Many Thanks

Mongolia

Answer: 1 in 36, the same as the original odds.

Why? No matter how many times the dice are rolled, the probability of
any particular combination neither increases or decreases because the
number of dice sides remains the same.

Bonus: The correct answer to 466945 was 33.3 %. Given that 1 out of
100 people would actually contract the disease and get a positive test
result, and 2 out of 100 people would receive a false positive test
result, the odds of the test result being correct are 1 in 3, or 33.3
%.

I don't know if the researchers aren't answering these questions
because they are sometimes homework questions, or what.

Mattzone
I am not sure if you misread the original question or simply do not
have an understanding of basic Probability theory. Yes you are of
course right in saying that the probability for EACH throw of the dice
is 1 in 36 (and yes
one throw is unaffected by another) However the question asked what is
the probability of getting AT LEAST 1 double six in 24 throws of the
dice. I
believe the answer PKUANKO and myself came up with (i.e. probability of .491)
is correct and furthermore this has been accepted by the original questioner.

Regarding your last comment about researchers not answering questions.
There are many reasons why a question may not be answered by a Google
researcher including the one you allude to (i.e. homework). In this
case however I tend to believe that the Google researchers did not
answer the
question as the relevant comments in effect answered the question. Any 
official answer could not really have added anything more to the question
and so an official answer in this case would have been inappropiate
and/or tacky. I also think your comment may have simply confused or
clouded the
answer to the original question.

Regarding your comment about question 466945, I will of course let the
participents in this particular question speak for themselves.

Many Thanks
Mongolia