A Machine Has Four Components, A, B, C, and D

question 235

Multiple Choice

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for themachine to work properly. Assume the probability of one part working does not depend on the functionality ofany of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.93,P(C) = 0.98, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to sixdecimal places.

• A) 0.999996
• B) 0.813698
• C) 0.000004
• D) 0.186302

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Definitions:

Environmental Conditions

The various physical and biological factors that influence an organism's life and development.

Phenotypic Response

The observable physical or biochemical changes in an organism in reaction to environmental factors.

Genotype

The genetic makeup of an organism, representing its set of genes.

Evolution by Natural Selection

A process where organisms better adapted to their environment tend to survive and produce more offspring, driving the evolution of species.