DRV Probabilities

Question

Suppose I have a 20-sided dice. What is the probability that in 5 rolls of the dice I get a number less than 6 exactly twice?

Answer 1

you can model this one as a binomial experiment where you have

p = 5/20 = 1/4

n = 5

x = 2

that makes the underlying formula here

P(x = 2) = C(5,2) * (0.25)^2 * (0.75)^3

P(x = 2) = 0.2637

meaning that you have about a 26.37% chance of this happening

Answer 2

P(X = 2), where X is the number of rolls getting a number less than 6.

This is Binomial probability since there are two outcomes: 1. less than 6, 2. greater than or equal to 6

P(getting less than 6) = 5/20 = 1/4

P(getting greater than or equal to 6) = 15 / 20 = 3/4

trial = n = 5

P(X=2) = 5 C 2 * (1/4) ^ 2 * (3/4) ^ 3 = 10 * 1/ (4^2) * 3^3 / 4^3 = .263671875 ~~.2637