Question

An assembly consists of two mechanical components. Suppose that the probabilities that the first and second components meet specifications are 0.96 and 0.87. Assume that the components are independent. Determine the probability mass function of the number of components in the assembly that meet specifications. X = number of components that meet specifications. Round your answers to four decimal places (e.g. 98.7654).

Answer 1

Explanation:

Given that an assembly consists of two mechanical components. Suppose that the probabilities that the first and second components meet specifications are 0.96 and 0.87.

Also the components are independent

If X - the number of components in the assembly that meet specifications, then we have x can take values as 0,1,2

P(X=0) = P(no component meets speficiations) =
`\\(1-0.96)(1-0.87)=0.04 *0.13\\=0.0052`

P(X=1) =P(either machine works with other machine not)

=
`P(AB')+P(A'B)\\= 0.96(0.13)+0.87(0.04)\\=0.1596`

P(x=2) = P(AB)=
`0.96*0.87\\=0.8352`