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Question
Solve the following problem :
The probability that a machine will produce all bolts in a production run within the specification is 0.9. A sample of 3 machines is taken at random. Calculate the probability that all machines will produce all bolts in a production run within the specification.
Solution
Let X denote the number of machines that run within specification.
P(a machine will produce all bolts in production run within the specification) = p = 0.9
∴ q = 1 – p = 1 – 0.9 = 0.1
Given, n = 3
∴ X ~ B(3, 0.9)
The p.m.f. of X is given by
P(X = x) = `""^3"C"_x (0.9)^x (0.1)^(3 - x),x` = 0, 1, 2, 3.
P(all machines will produce all bolts in a production run within the specification)
= P(X = 3)
= `""^3"C"_3 (0.9)^3 (0.1)^0`
= 0.729
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