Question

A shipment of thirteen smartphones contains three with cracked screens. if sold in a random order, what is the probability that the first ten sold have undamaged screens?

Answer 1

The probability of a screen being damaged is:
P(d)=3/13=0.23
Thus to get the probability that the first 10 sold were undamaged we use the binomial distribution formula:
P(x)=n!/((n-x)!x!)p^x(1-p)^(n-x)
from the question:
n=13, x=10, p=0.23
hence
P(x)=13!/((13-10)!10!)*0.23^(13-10)*(1-0.23)^(10)
simplifying the above we get:
P(x)=0.255