Probability of Rolling at Least One 1 with Ten Dice

To calculate the probability that at least one '1' appears when rolling ten fair dice, we can use the concept of complementary probability.

The complementary probability is the probability that an event does not occur. In this case, we want to find the probability that no '1' appears when rolling the ten dice.

The probability of not rolling a '1' on a single die is 5/6, as there are five possible outcomes (2, 3, 4, 5, 6) out of six total outcomes (1, 2, 3, 4, 5, 6).

Since the dice rolls are independent events, the probability of not rolling a '1' on all ten dice is (5/6)^10.

To find the probability that at least one '1' appears, we subtract the complementary probability from 1:

Probability of at least one '1' = 1 - (5/6)^10

Now, let's calculate this probability:

Probability of at least one '1' ≈ 1 - 0.1615 ≈ 0.8385

Therefore, the probability that at least one '1' appears when rolling ten fair dice is approximately 0.8385.