Question

all of the steps on a certain ladder fail 2% of the time. If Maria is going to climb up all 23 steps, what is the probability that none of the steps will fail?

Answer 1

Let $X=$ the number of the steps which will fail: $X\in Bin (n, p)$

$$p(X=x)=\dbinom{n}{x}p^x(1-p)^{n-x}$$

Given $p=0.02, n=23$

$$p(X=0)=\dbinom{23}{0}(0.02)^0(1-0.02)^{23-0}$$

$$=(0.98)^{23}\approx0.628347$$