An assembly consists of two mechanical components. Suppose that the probabilities that the first and second components meet specifications are 0.99 and 0.91. 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).

P[X=0] = 0.0009

P[X=1] = 0.0982

P[X=2] = 0.9009

Step-by-step explanation:

Let X represent the number of components that meet specification.

Since there are only two components in an assembly, X can take on the values of 0, 1, and 2.

The probability that first component will meet specification, P(A) = 0.99.

Therefore, the probability that the first component does not meet specification, P(A') = 1- 0.99 = 0.01

The probability that second component will meet specification, P(B) = 0.91

Therefore, the probability that the second component does not meet specification, P(B') = 1- 0.91 = 0.09

Therefore, the probability mass function of X is:

a) The probability that two components do not meet specification

P[X = 0] = (0.01)(0.09) = 0.0009

b) The probability that only one of the two components meets specification

P[X = 1] = P(A)P(B') + P(A')P(B) = (0.99)(0.09) + (0.01)(0.91) = 0.0982

c) The probability that the two components meet specification

P[X = 2] = P(A)P(B) = (0.99)(0.91) = 0.9009

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