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Re: Gambling with 4 dice, what is the probability of getting an [#permalink]
24 May 2012, 00:52
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cyberjadugar 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
Looking for a one-liner answer...
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.
\(P=\frac{3^4+3^4+6*3^4}{6^4}=\frac{1}{2}\).
Answer: B.
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.
Re: Gambling with 4 dice, what is the probability of getting an [#permalink]
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.
Re: Gambling with 4 dice, what is the probability of getting an [#permalink]
24 May 2012, 01:30
Expert's post
cyberjadugar wrote:
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.
Re: Gambling with 4 dice, what is the probability of getting an [#permalink]
01 May 2015, 02:02
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Re: Gambling with 4 dice, what is the probability of getting an [#permalink]
01 May 2015, 02:02
Bunuel wrote:
cyberjadugar 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
Looking for a one-liner answer...
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.
\(P=\frac{3^4+3^4+6*3^4}{6^4}=\frac{1}{2}\).
Answer: B.
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.
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