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Gambling with 4 dice, what is the probability of getting an even sum?
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20 Apr 2022, 13:14
20 Apr 2022, 13:14
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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
A. 3/4
B. 1/2
C. 2/3
D. 1/4
E. 1/3
Re: Gambling with 4 dice, what is the probability of getting an even sum?
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22 Apr 2022, 02:41
22 Apr 2022, 02:41
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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.
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.
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Re: Gambling with 4 dice, what is the probability of getting an even sum?
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18 Oct 2022, 09:58
18 Oct 2022, 09:58
1
Given that we are Gambling with 4 dice and We need to find what is the probability of getting an even sum?
At each stage there is only two possibility of getting a sum. Either the sum can be even or odd.
Out of the siz numbers we have exactly 3 odd and exactly 3 even
=> Probability of getting an even or getting an odd sum at any stage will be same and will be equal to \(\frac{1}{2}\)
=> Probability of getting an even sum = \(\frac{1}{2}\)
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
At each stage there is only two possibility of getting a sum. Either the sum can be even or odd.
Out of the siz numbers we have exactly 3 odd and exactly 3 even
=> Probability of getting an even or getting an odd sum at any stage will be same and will be equal to \(\frac{1}{2}\)
=> Probability of getting an even sum = \(\frac{1}{2}\)
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
