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
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.