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# Gambling with 4 dice, what is the probability of getting an

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Joined: 28 Mar 2012
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Location: India
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Gambling with 4 dice, what is the probability of getting an [#permalink]

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24 May 2012, 00:31
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61% (02:26) correct 39% (01:24) wrong based on 162 sessions

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Gambling with 4 dice, what is the probability of getting an even sum?

A. 3/4
B. 1/2
C. 2/3
D. 1/4
E. 1/3
[Reveal] Spoiler: OA
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Kudos [?]: 93078 [4] , given: 10542

Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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24 May 2012, 00:52
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Gambling with 4 dice, what is the probability of getting an even sum?

A. 3/4
B. 1/2
C. 2/3
D. 1/4
E. 1/3

Even sum can be obtained in following cases:
EEEE - one case. Each E can take 3 values (2, 4, or 6), so total for this case is 3^4;
OOOO - one case. Each O can take 3 values (1, 3, or 5), so total for this case is 3^4;
EEOO - $$\frac{4!}{2!2!}=6$$ cases (EOEO, OOEE, ...). Each E can take 3 values (2, 4, or 6) and each O can also take 3 values (1, 3, or 5), so total for this case is 6*3^2*3^2=6*3^4;

Total # of outcomes when throwing 4 dice is 6^4.

$$P=\frac{3^4+3^4+6*3^4}{6^4}=\frac{1}{2}$$.

Even without any math: the probability of getting an even sum when throwing 4 dice is the same as getting an even number on one die, so it must be 1/2.

Similar problem to practice: a-box-contains-100-balls-numbered-from-1-to-100-if-three-b-109279.html

Hope it helps.
_________________
Joined: 28 Mar 2012
Posts: 314
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GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 29

Kudos [?]: 398 [0], given: 23

Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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24 May 2012, 01:26
Hi Bunuel,

The shortcut is perfect! Are you aware of any thread where we such approaches are discussed?

Similar solution can be applied to problem like no. of cases A occurs before B in a sequence, no. of cases where A & B are together
In both cases half of the total no. of cases would be the answer. Since, either A comes after B or before B, either A & B are together or separated.

Regards,
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Kudos [?]: 93078 [0], given: 10542

Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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24 May 2012, 01:30
Expert's post
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Hi Bunuel,

The shortcut is perfect! Are you aware of any thread where we such approaches are discussed?

Similar solution can be applied to problem like no. of cases A occurs before B in a sequence, no. of cases where A & B are together
In both cases half of the total no. of cases would be the answer. Since, either A comes after B or before B, either A & B are together or separated.

Regards,

DS questions on probability: search.php?search_id=tag&tag_id=33
PS questions on probability: search.php?search_id=tag&tag_id=54

Hope it helps.
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Kudos [?]: 113 [0], given: 812

Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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06 Feb 2013, 03:14
very hard, I want to follow this post. this is 51/51 level , I think
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Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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27 Feb 2013, 04:06
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probability for EEEE to happen is

1/2*1/2*1/2*1/2=A

similarly probability for OOOO and OOEE, OEOE,...(there are 6 cases)

total 8 case

add 8 cases we have 8/A=1/2

is the result.
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Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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01 May 2015, 02:02
Hello from the GMAT Club BumpBot!

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Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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01 May 2015, 02:02
Bunuel wrote:
Gambling with 4 dice, what is the probability of getting an even sum?

A. 3/4
B. 1/2
C. 2/3
D. 1/4
E. 1/3

Even sum can be obtained in following cases:
EEEE - one case. Each E can take 3 values (2, 4, or 6), so total for this case is 3^4;
OOOO - one case. Each O can take 3 values (1, 3, or 5), so total for this case is 3^4;
EEOO - $$\frac{4!}{2!2!}=6$$ cases (EOEO, OOEE, ...). Each E can take 3 values (2, 4, or 6) and each O can also take 3 values (1, 3, or 5), so total for this case is 6*3^2*3^2=6*3^4;

Total # of outcomes when throwing 4 dice is 6^4.

$$P=\frac{3^4+3^4+6*3^4}{6^4}=\frac{1}{2}$$.

Even without any math: the probability of getting an even sum when throwing 4 dice is the same as getting an even number on one die, so it must be 1/2.

Similar problem to practice: a-box-contains-100-balls-numbered-from-1-to-100-if-three-b-109279.html

Hope it helps.

I can not say any word for this excellency
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Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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24 Jun 2016, 14:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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06 Jul 2016, 10:48
I got it wrong. Why am I wrong?
e+e=e
o+o=e
e+o=o

So it's even in 2/3 of the times.
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Posts: 36545
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Kudos [?]: 93078 [0], given: 10542

Re: Gambling with 4 dice, what is the probability of getting an [#permalink]

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07 Jul 2016, 03:38
Mariwa wrote:
I got it wrong. Why am I wrong?
e+e=e
o+o=e
e+o=o

So it's even in 2/3 of the times.

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Re: Gambling with 4 dice, what is the probability of getting an   [#permalink] 07 Jul 2016, 03:38
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