Re: Gambling with 4 dice, what is the probability of getting an even sum?
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22 Apr 2022, 02:41
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.