A die is rolled 12 times. Find the chance that the face with six spots appears once among the first 6 rolls, and once among the next 6 rolls.

Question

kropot72 · Answer

The chance of a particular number not coming up in a roll of the die is 5/6. The probability of 6 not appearing in 5 out of 6 rolls is
$$(\frac{5}{6})^{5}$$

kropot72 · Answer

The events 'the face with six spots appears once among the first 6 rolls' and 'the face with six spots appears once among the next 6 rolls' are independent. Therefore the probability of both occurring is the product of the individual probabilities:
$$Required\ probability=(\frac{5}{6})^{5}\times (\frac{5}{6})^{5}=(\frac{5}{6})^{10}$$

anonymous · Answer

I understand the approach, but i have 2 small questions:
1. isn't supposed to be (5/6)^6 ?
2. isn't supposed to be at the end P(one-6) = 1-P(no-6)?
Thanks!