PiyushK wrote:

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.

A. 31/36

B. 31/76

C. 5/36

D. 45/76

E. 1/9

Dear

PiyushK,

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 and "

dice" 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?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)