In a dice game, the only way that a player wins on her second turn is

Question

In a dice game, the only way that a player wins on her second turn is if the sum of the dice she rolls on her second turn matches the sum from her first. On each turn, a player simultaneously rolls two, fair, six-sided dice. If Lindsey's total from her first turn is 6, what is the probability that she will win on her second turn?

A. 1/12
B. 5/36
C. 1/6
D. 7/36
E. 17/36

Kudos for a correct solution.

A. 1/12
B. 5/36
C. 1/6
D. 7/36
E. 17/36

chetan2u · Answer

ANS B 5/36....
way to get sum as 6..(1,5)(5,1)(2,4)(4,2)(3,3)
so 5/36

gmat6nplus1 · Answer

call dice_1 a; call dice_2 b --> a+b = 6; few cases unfold

1) a=1 and b=5 probability is 1/36(2) we multiply by two to include the case in which b=1 and a=5
2) a=2 and b=4 again probability 1/18 
3) a=3 and b=3 probability 1/36

since every one of these cases is equally likely to yield the wanted result --> 1/18(2)+1/36 = 5/36

Answer B.

Cadaver · Answer

5/36......(1,5)(5,1)(2,4)(4,2)(3,3)

CCMBA · Answer

To win, she must roll a 6 on her second turn.

Pr(x+y = 6) = 2*Pr(1 + 5) + 2*Pr(2+4) + Pr(3+3) = 2(1/6)^2 + 2(1/6)^2 + (1/6)^2 = 5/36

There are 2 ways to roll 1 and 5, and 2 ways to roll 2 and 4 because order matters.

CCMBA · Answer

To win, she must roll a 6 on her second turn.

Pr(x+y = 6) = 2*Pr(1 + 5) + 2*Pr(2+4) + Pr(3+3) = 2(1/6)^2 + 2(1/6)^2 + (1/6)^2 = 5/36

There are 2 ways to roll 1 and 5, and 2 ways to roll 2 and 4 because order matters.

KarishmaB · Answer

Note that the question has been written to feel more complicated than it actually is. We have no relevance of first turn or second turn. The question simply says that two dice will be rolled and what is the probability that the sum rolled is 6?

We obtain 6 in 3 ways - 1 and 5, 2 and 4, 3 and 3.

Now assume that the dice are distinct i.e. one red and the other yellow. So you can get the sum of 6 in the following ways
1 on Red, 5 on Yellow or the other way around - 2 ways
2 on Red, 4 on Yellow or the other way around - 2 ways
3 on Red, 3 on Yellow - 1 way

Total 5 ways.

There are a total of 6*6 = 36 ways in which we can get different numbers on the roll of 2 distinct dice.

Hence, probability = 5/36

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Since six things can happen on each individual roll, and she'll roll two dice, there are 6(6) = 36 total possibilities for the denominator. Then you need to count how many ways she can win, which are:

1 and 5

2 and 4

3 and 3

4 and 2

5 and 1

Accordingly, 5 of the 36 outcomes allow Lindsey to win, so her probability is 5/36.

HunterJ · Answer

Can someone please explain why we count the outcome   only once? There are two die,   can occur two different ways, it seems to me.

EMPOWERgmatRichC · Answer

Hi joejackson,

It helps to think about the possible outcomes in the format "first die, second die":

To get a total of 6, you need to have one of the following outcomes (presented in 'first, second' format):

1 and 5
2 and 4
3 and 3
4 and 2
5 and 1

That's a total of 5 'winning' outcomes out of 36 possible outcomes.

GMAT assassins aren't born, they're made,
Rich

KarishmaB · Answer

Yes, say the two dice are distinct in colour - say one is red and the other is yellow. 
You can get 2 on the Red one and 4 on the Yellow one. This is different from 2 on the Yellow one and 4 on the Red one - fine
How about this? You get 3 on the Red one and 3 on the Yellow one. How is it any different from 3 on the Red one and 3 on the Yellow one? They are the same case, right? So you should count it only once.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In a dice game, the only way that a player wins on her second turn is

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a dice game, the only way that a player wins on her second turn is

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards