Question

A factory manufactures machines. Each machine is defective with probability 1/100, independently. The machines get numbered...

A factory manufactures machines. Each machine is defective with probability 1/100, independently.

The machines get numbered 1, 2, . . . as they’re produced
(a) Out of machines 1, . . . , 1000, what is the probability that none are defective?
(b) Out of machines 1, . . . , 1000, what is the probability that two or fewer are defective? (
c) Out of machines 1, . . . , 1000, what is the probability that exactly ten are defective?
(d) What is the probability that the first defective machine is number 17?
(e) What is the probability the first defective machine is numbered 18 or higher?

Math   Statistics-And-Probability   
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Answer #1

There are 1000 machines and Probability of each machine being defective is 0.01

Let X be the number of defective machines. In that case,

(a)

(b)

c)

Here,

d)

e)

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