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

1. 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?

Solutions

Expert Solution

Let X denote the number of defectives in the set. Then

Required probability =

Let X denote the number of defectives in the set. Then

Required probability =

Let X denote the number of defectives in the set. Then

Required probability =

Required probability = P(first 16 are non-defective and 17th is defective)

Required probability = P(first defective is numbered 18 or higher)

= P(18th is the first defective) + P(19th is the first defective) + P(20th is the first defective) + ....+P(1000th is the first defective)

orchestra answered 1 year ago

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