In the tabletop role-playing game Dungeons & Dragons, players decide the outcome
ID: 3180569 • Letter: I
Question
In the tabletop role-playing game Dungeons & Dragons, players decide the outcomes of events by rolling a fair 20-sided die (the sides are numbered from 1 to 20). The outcome of rolling a 20 is known as a "critical success" and the outcome of rolling a 1 is known as a "critical failure".
(a). In the long run, how often will the outcome be a critical success of a critical failure?
(b). What is the probability of getting a critical success or critical failure in 10 rolls? [Hint: First compute the probability of getting no 1's or 20's in 10 rolls]
Explanation / Answer
Solution:-
a) The probability of outcome of a critical success is 0.05
Total number of outcomes in die = 20
Number of critical success = 1
The probability of outcome of a critical success = 0.05
Total number of outcomes in die = 20
Number of critical success = 1
The probability of outcome of a critical failure = 0.05
b) The probability of getting a critical success or critical failure in 10 rolls is 0.6513.
The probability of getting a critical success or critical failure in one rolls is 0.10
n = 10
p = 0.10
By applying binomial distribution:-
P(x = n) = nCx*px *(1 - p)(n - x)
P(x > 1) = 0.6513
The probability of getting a critical success or critical failure in 10 rolls is 0.6513