A and B in turns, throw a dice. If A gets a sum of 8 before B gets a sum of 9, then A wins. But if B gets a sum on 9 before A gets a sum of 8, then B wins. Find the chances of winning of A.
I find a few things unclear about this particular question. I point out that a good GMAT Quant question is very tight, and leaves not a single ambiguity --- it can be difficult to write a Quant question to those standards. Question #1
: you say "a dice
" ---- that's grammatically incorrect and, hence unclear. The word "die
" is singular
" is plural
. When I first glanced at the question, I assumed you meant --- each person was throwing two dice, and on each new throw, the question was: is the current sum an 8 or 9. That game could go on for quite some time, and calculating that is quite challenging (in that game, I found A has a 5/9 chance of winning). Upon re-reading, it appeared to me that you meant: each was throwing a single die. If this is correct, that leads me to ....Question #2
: Suppose A rolls a 6 on the first roll, then another 6 on the second roll, for a sum of 12. Does this count as winning? In other words, it is a matter of getting to a sum of 8 or more
, before B gets to 9 or more
? Or, do you mean that the game continues until, say, A has a string of consecutive rolls that has the exact
sum of eight? (This latter question would be one of the hardest probability questions I have seen or imagined!) Question #3
: It's not explicit, but I am inferring that the rolls are not simultaneous, but rather, that A rolls once first, then B rolls once, then A rolls again, then B rolls again, etc. This was my take on the rolling procedure, but it is not made explicit in the question.
I can't even begin to think about finding an answer until I know the answer to all of these questions.
All of these are ambiguities that must be explicitly address in the way the problem is formulated. Does all this make sense?
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