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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
Probability of defective watch out of 100 watches = `10/100 = 1/10`.
Here, n = 8
p = `1/10`
q = `1 - 1/10 = 9/10`
And r ≥ 1
P(X ≥ 1) = 1 – P(x = 0)
= `1 - ""^8"C"_0 (1/10)^0 (9/10)^(8 - 0)`
= `1 - (9/10)^8`
Hence, the required probability is `1 - (9/10)^8`.
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