Question

The probability of exactly no successes in five trials of a binomial experiment in which
p =
1
4

Answer 1

P=1/4

Answer 2

If the probability of success is 1/4, then the probability of failur is 1 - (1/4) = 4/4 - 1/4 = 3/4

Answer 3

Since we have five trials with no successes, ie 5 failures, this means that the probability of this happening is

(3/4)*(3/4)*(3/4)*(3/4)*(3/4)

I'll let you compute that. Notice how there are 5 copies of 3/4

Answer 4

as a shortcut, you can compute (3/4)^5