- #1
mateomy
- 305
- 0
If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls?
So this problem is hard to wrap my head around. I'm probably wrong on many counts, here's what I'm doing:
Two fair dice are rolled 10 times but this question only cares about 5 of them. Because there's two dice I have,
<br /> \frac{1}{6} \frac{1}{6} = \frac{1}{36}<br />
for my probability of getting a 6.
Because they're asking 'at least one 6', I feel it's appropriate to take the complement.
<br /> 1 - \sum_{i = 0}^{1} \left(5 \choose i \right)\left(\frac{1}{36}\right)^{i} \left(1 - \frac{35}{36}\right)^{5 - i}<br />
However, when I do this my answer is off by about 0.03. So I know something isn't right. I'm not even sure if I'm attacking this correctly. Need clarification. Thanks.
So this problem is hard to wrap my head around. I'm probably wrong on many counts, here's what I'm doing:
Two fair dice are rolled 10 times but this question only cares about 5 of them. Because there's two dice I have,
<br /> \frac{1}{6} \frac{1}{6} = \frac{1}{36}<br />
for my probability of getting a 6.
Because they're asking 'at least one 6', I feel it's appropriate to take the complement.
<br /> 1 - \sum_{i = 0}^{1} \left(5 \choose i \right)\left(\frac{1}{36}\right)^{i} \left(1 - \frac{35}{36}\right)^{5 - i}<br />
However, when I do this my answer is off by about 0.03. So I know something isn't right. I'm not even sure if I'm attacking this correctly. Need clarification. Thanks.