you take one roll of a 20-sided number cube to determine your fate. if you roll a number greater than or equal to 8, you are able to defeat the troll. But if you roll a prime number, the bridge will give out with you still on it. What are orgoth's chances of safely reaching the other side of the canyon

Answer 1

Orgoth's chances of safely reaching the other side of the canyon are:

P(roll >= 8 AND not prime) = P(roll >= 8) - P(roll >= 8 AND prime)

The probability of rolling a number greater than or equal to 8 is 13/20, since there are 13 numbers from 8 to 20 on a 20-sided cube.

The probability of rolling a prime number is 8/20, since there are 8 prime numbers on a 20-sided cube (2, 3, 5, 7, 11, 13, 17, 19).

Therefore, Orgoth's chances of safely reaching the other side of the canyon are:

P(roll >= 8 AND not prime) = 13/20 - 8/20 = 5/20 = 1/4

So Orgoth has a 1 in 4 chance of safely reaching the other side of the canyon.