Question

An assembly consists of two mechanical components. Suppose that the probabilities that the first and second components meet specifications are 0.98 and 0.85. 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.

Answer 1

The probability mass function is given by

P(X = 0) = 0.003, P(X = 1) = 0.164, P(X = 2) = 0.833

Explanation:

Given to us are two mechanical components.

The probability of the first component meeting the given specifications are 0.98.

The probability that the second component meets the given specifications = 0.85.

In the information given the components are said to be independent.

The probability mass function will be calculated in the following way

i.) P(X=0) which is the probability that neither of the components meet the specifications.

ii) P(X=1) which is the probability when either of the components will meet the specifications and the other will not.

iii) P(X=2) which is the probability that both components meet the specification.

Therefore P(X = 0) = ( 1 - 0.98) × ( 1 - 0.85) = 0.02 × 0.15 = 0.003

and, P(X = 1) = (0.98 × ( 1 - 0.85)) + (( 1 - 0.98) × 0.85)

= (0.98 × 0.15) + (0.02 × 0.85)

= 0.147 + 0.017

= 0.164

and finally, P(X=2) = (0.98 × 0.85)

= 0.833