Hi Rich,[email protected] wrote:Hi lheiannie07,
This is a tougher probability question than average (and you likely will not see this exact situation on Test Day). This is meant to say that you shouldn't be too concerned about this prompt until you're picking up points in all the other 'gettable' areas first.
That having been said, the 'quirk' with this question is that you have to account for the probability of rolling two dice and getting the same number on both dice vs. getting two different numbers.
When rolling two dice, there are 36 possible outcomes:
-6 outcomes have the same number twice (1-1, 2-2, etc.)
-30 outcomes have two different numbers (1-4, 3-2, 5-1, etc.)
Thus, 6/36 = 1/6 of the outcomes are the same number twice
30/36 = 5/6 of the outcomes are two different numbers
IF Pam rolled 5-5, then Robin would have to also roll 5-5. The probability of that occurring would be: (1/6)(1/6) = 1/36.
IF Pam rolled 2-6, then Robin has two different ways to match up (2-6 OR 6-2). The probability of that occurring would be (2/6)(1/6) = 2/36 = 1/18
Accounting for all possible outcomes, the probability of Pam and Robin rolling the same result would be:
(1/6)(1/36) + (5/6)(1/18) =
1/216 + 5/108 =
1/216 + 10/216 =
11/216
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
Dear Rich,[email protected] wrote:Hi Mo2men,
The prompt asks for the probability that both women will roll the same two numbers - but no emphasis is placed on the ORDER of the numbers. So if Pam rolls 2-6, then EITHER of Robin's dice could be the 2 and the other would then have to be the 6 (thus 2-6 or 6-2 would be a 'match').
Imagine if we rolled one die at a time. The probability of rolling a 2 OR a 6 on the first die is 2/6.
Assuming that first roll is a 'match' (either the 2 or the 6), then the second die would have to be the other number - and the probability of THAT happening would be 1/6.
(2/6)(1/6) = 2/36 = 1/18
GMAT assassins aren't born, they're made,
Rich
You can consider a 2-6 as equal to 6-2, but you have to recognize that there are 2 ways to achieve this, so it doesn't make any difference if you view them as distinct or identical.Mo2men wrote:Dear Rich,[email protected] wrote:Hi Mo2men,
The prompt asks for the probability that both women will roll the same two numbers - but no emphasis is placed on the ORDER of the numbers. So if Pam rolls 2-6, then EITHER of Robin's dice could be the 2 and the other would then have to be the 6 (thus 2-6 or 6-2 would be a 'match').
Imagine if we rolled one die at a time. The probability of rolling a 2 OR a 6 on the first die is 2/6.
Assuming that first roll is a 'match' (either the 2 or the 6), then the second die would have to be the other number - and the probability of THAT happening would be 1/6.
(2/6)(1/6) = 2/36 = 1/18
GMAT assassins aren't born, they're made,
Rich
Thanks for your reply. However, it proved that either the question wording is unclear or my assumptions are wrong.
When you rolling pair of dice, do you consider rolling them one by one or both in same time. The reason of question is the that PAM rolls pair of dice in one shot and gets 2-6. Then, Robin rolls her pair of dice in one shot. So it is nonsensical to assume if she get 2-6 or 6-2 as both are same. At the end, pair of dice is thrown at SAME time.
The case you describe happens when Pam a die by die then Robin rolls die by die so in first she can get 2 or 6 and the other die would be the other number. Now it makes sense if that the case in question.
How can you detect which scenario from my above explanation, if I'm correct.
I hope you understand my confusion and help.
Thanks in advance for your suppport
We need to determine the probability that when Pam and Robin each rolls a pair of fair, six-sided dice, they both roll the same set of numbers. There are two scenarios: when Pam and Robin both roll the same two numbers and when they roll two distinct numbers.lheiannie07 wrote:Pam and Robin each roll a pair of fair, six-sided dice. What is the probability that Pam and Robin will both roll the same set of two numbers?
A. 1/216
B. 1/36
C. 5/108
D. 11/216
E. 1/18
