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?

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