Question:
A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, what is the probability that there will be at least one defective watch?
Solution:
Given: Total number of watches = 100 and number of defective watches = 10
So, the probability of selecting a detective watch = 10/100 = 1/10
Now,
n = 8, p = 1/10 and q = 1 – 1/10 = 9/10, r ≥ 1
P(X ≥ 1) = 1 – P(x = 0) = 1 – 8C0 (1/10)0(9/10)8 – 0 = 1 – (9/10)8
Therefore, the required probability is 1 – (9/10)8.