A lot of 100 watches is known to have 10 defective watches.
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.

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