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What is the probability of getting a sum of 8 or 14 when

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Bunuel
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Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post   03 Feb 2017, 07:10
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sharkr wrote:
gayathri wrote:
What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?

A. 1/6
B. 1/4
C. 1/2
D. 21/216
E. 32/216



If we're rolling 3 dice simultaneously, why is it that we're counting, for example, (6,1,1) as 3 ways?
Is it assumed that 3 dice are distinguishable?


Yes. Consider the die to be red, blue and green. Then 6, 1, 1 can occur in 3 ways:

red - blue - green
6 - 1 - 1
1 - 6 - 1
1 - 1 - 6.
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Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post   09 Aug 2017, 05:18
I dont understand why there are only three ways to roll (1,1,6). There are three difference dices; therefore there is supposed to be 6 ways.
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Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post   09 Apr 2018, 10:59
Snooopy wrote:
I dont understand why there are only three ways to roll (1,1,6). There are three difference dices; therefore there is supposed to be 6 ways.


1, 1, 6
1, 6, 1
6, 1, 1

3 ways
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Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post   21 Sep 2018, 10:10
gayathri wrote:
gmat+obsessed wrote:
Is there any other to solve this question ?


The other way would be to list out each option.
The options for a sum of 8: (6,1,1) has 3 options ie (6,1,1), (1,6,1), (1,1,6); (5,2,1) has 6 options, (4,3,1) has 6 options, (4,2,2) has 3 options, (3,3,2) has 3 options. We have 21 options to get 8.

The options for a sum of 14: (6,4,4) has 3 options, (6,5,3) has 6 options, (6,6,2) has 3 options, (5,5,4) has 3 options. We have 15 options to get 14.

Total: 21+15= 36/216 = 1/6.


Hi

Can you please explain why there are 6 options as opposed to 3 options(3 re-arrangements)?

Thanks
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Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post   21 Sep 2018, 19:09
chetan2u Bunuel VeritasKarishma

Hello experts,

I was wondering is there any easier way to solve this problem instead of listing out each possibility?

Thank You!
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Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post   22 Sep 2018, 01:28
Samawasthi wrote:
gayathri wrote:
gmat+obsessed wrote:
Is there any other to solve this question ?


The other way would be to list out each option.
The options for a sum of 8: (6,1,1) has 3 options ie (6,1,1), (1,6,1), (1,1,6); (5,2,1) has 6 options, (4,3,1) has 6 options, (4,2,2) has 3 options, (3,3,2) has 3 options. We have 21 options to get 8.

The options for a sum of 14: (6,4,4) has 3 options, (6,5,3) has 6 options, (6,6,2) has 3 options, (5,5,4) has 3 options. We have 15 options to get 14.

Total: 21+15= 36/216 = 1/6.


Can you please explain why there are 6 options as opposed to 3 options(3 re-arrangements)?

Thanks


Hi Samawasthi

When we are taking the possibility of suppose (6,6,2), the number of ways to arrange these 3 numbers would be 3!/2! = 3 ways (Divided by 2! because 6 is repeated twice)
(6,6,2) can be written as (2,6,6), (6,6,2) and (6,2,6) - 3 options/ways.

When we are taking possibility of suppose (6,5,3), the number of ways to arrange these 3 different numbers would be 3! = 6 ways (We have no similar numbers)
(6,5,3) can be written as (6,5,3), (5,6,3), (6,3,5), (3,5,6), (3,6,5) and (5,3,6) - 6 options/ways
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Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post   22 Sep 2018, 08:17
i did it manually. But if you look at pattern it is easy
so three dices are rolled. We need the sum to be 8 or 14
start systematically
Sum = 8
161 251 341 431 521 611
152 242 332 422 512
143 233 323 413
134 224 314
125 215
116
Total = 21 nos
Sum =14
266
356 365
446 455 464
536 545 554 563
626 635 664 653 662
Total = 15 Nos
hence total cases = 21+15 = 36

Hence the probability = 36/216 = 1/6 Answer
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What is the probability of getting a sum of 8 or 14 when [#permalink] New post   23 Apr 2019, 08:23
Richie Weasel wrote:
Quote:
"Gayathri"
What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?

a) 1/6
b) 1/4
c) 1/2
d) 21/216
e) 32/216

Is there a shorter way to do this than listing each possibility?


I am confident that there is a better way, but I looked at the first few possibilities

throw a 3 - 1 way
throw a 4 - 3 ways
throw a 5 - 6 ways
throw a 6 - 10 ways

and recognized these as triangular numbers (the series could also be identified as add 2, add 3, add 4 ...).

from there it was easy to calculate that there are 21 ways to hit an 8 and 15 ways to hit a 14. (Problems with fair dice and coins produce symmetrical probability distributions, so one can count down from 1 way to throw an 18)

[more than 2 minutes - less than 3 minutes][/

How did you get 15 ways to get a 14?
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What is the probability of getting a sum of 8 or 14 when [#permalink] New post   14 Nov 2019, 03:59
gayathri wrote:
What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?

A. 1/6
B. 1/4
C. 1/2
D. 21/216
E. 32/216


TOTAL OUTCOMES: \(6^3=216\)

POSSIBLE OUTCOMES: for sum of 8 and 14 \(=36\)

[116=8]: arrangements(3!/2!)=3
[125]: arrangements(3!)=6
[134]: 6
[224]: 3
[233]: 3
Possible outcomes for sum of 8: 3+6+6+3+3=12+9=21

[662=14]: 3
[653]: 6
[644]: 3
[554]: 3
Possible outcomes for sum of 14: 3+6+3+3=6+9=15

PROBABILITY: (possible/total)=36/216=12/72=4/24=1/6

Ans (A)
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Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post   21 Sep 2023, 01:58
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