Two fair dice are thrown together. what is the probability that the nu

Question

Two fair dice are thrown together. what is the probability that the number obtained on one of the dice is a multiple of the number obtained on the other die?

A) 11/18
B) 5/18
C) 5/9
D) 8/9

KarishmaB · Accepted Answer

You can go the other way around:
Find the pairs in which neither is a multiple of the other. 
Ignore all pairs with 1 since the other number will be a multiple of 1.

If one number is 2, the other can be 3 or 5. So two possible options. We could have 2 on the other die so total 4 options (2, 3) (2, 5), (3, 2), (5, 2).

If one number is 3, the other can be 4 or 5. Again, there will be 4 total options.

If one number is 4, the other can be 5 or 6. Again, there will be 4 total options.

If one number is 5, the other can be 6. There will be total 2 options.

There are total 4 + 4 + 4 + 2 = 14

Probability that neither is a multiple of the other = 14/36 = 7/18

Probability that one number is a multiple of the other = 1 - 7/18 = 11/18

Answer (A)

EMPOWERgmatRichC · Answer

Hi rverma007,

What is the source of this question? I ask because you've listed just 4 answer choices, which is not realistic. If you're studying from material that is not proper GMAT material, then you could very well be hurting your chances at scoring at a high level on the Official GMAT.

Regardless, here's how to answer this question. Each of the two dice has 6 possible outcomes (1 - 6, inclusive), so there are (6)(6) = 36 possible pairs of dice rolls.

We have to figure out how many of those pairs include a number that is a multiple of the other number. We can list them out:

1,6 and 6,1
1,5 and 5,1
1,4 and 4,1
1,3 and 3,1
1,2 and 2,1
1,1

2,6 and 6,2
2,4 and 4,2
2,2

3,6 and 6,3
3,3

4,4
5,5
6,6

22 of the 36 options fit the description of what we're looking for. 22/36 = 11/18

Final Answer:  A

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

BrushMyQuant · Answer

Given that Two fair dice are thrown together and we need to find what is the probability that the number obtained on one of the dice is a multiple of the number obtained on the other die?

As we are rolling two dice => Number of cases =  6^2  = 36

Lets start writing the possible cases where number of one dice is a multiple of other

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)  
(2,1), (2,2), (2,4), (2,6)
(3,1), (3,3), (3,6)
(4,1), (4,2), (4,4)
(5,1), (5,5)
(6,1), (6,2), (6,3), (6,6)

=> 22 cases

=> Probability that the number obtained on one of the dice is a multiple of the number obtained on the other die =  \frac{22}{36}  =  \frac{11}{18}

So,  Answer will be A 
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

Purnank · Answer

When 2 fair dice thrown together, sample space is 36.
 
For such 2 numbers (_ _) only possible combinations are as below
for 1 - there are total 11 posibilities (1,1) (1,2) ..... (1,6) (6,1) (5,1)....... (2,1)
for 2, there are 5 possibilities - (2,2) (2,4) (2,6) (4,2) (6,2)
similarly for 3 there will be 3 (3,3) (3,6) (6,3)
and for 4,5,6 there will be 1 for each so total - 3
So total possibilities = 11 + 5 + 3 + 3 = 22
Probability = 22/36 = 11/18
  Answer is A.

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.

Two fair dice are thrown together. what is the probability that the nu

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

Two fair dice are thrown together. what is the probability that the nu

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