342 1ST TEST IN PROBABILITY THEORY AND STATISTICs 195 Variant 1 Calculate reliab

Question

342 1ST TEST IN PROBABILITY THEORY AND STATISTICs 195 Variant 1 Calculate reliability of the system of four components, connected in parallel, if each component is operable with probability 0.93 independently on other components. A coin is tossed 120 times. Find the probability for the event that head side is obtained a) 58 times, b) more than 62 times, c) between 40 and 61 times. A computer assembling company receives 27% of parts from supplier supplier Y, and the remaining parts from supplier. 9% of parts supplied by supplied by Y, and 5% of parts supplied by Z are defective. Compute the probability th ssembled computer has not a defect. X, 38% of parts fron X, 3% of par he probability that a component does not conform a standard is 0.08. Compute robability that at least 2 components from 20 are nonstandard. mong 23 computers in some store, 7 have defects. 5 randomly selected computer ught for the university lab. Compute the probability that all five computers ha fects

Explanation / Answer

Question 1:

Here we are given that each of the component works with a probability of 0.93, therefore probability that a component does not work is computed as: = 1 - 0.93 = 0.07

Now the reliability of the system that is the probability that the system works is computed as:

= 1 - Probability that the system does not work

= 1 - Probability that all 4 components dont work

= 1 - 0.07*0.07*0.07*0.07

= 0.99997599

Therefore the reliability of the system here is 0.99997599

Note that in a parallel combination the system does not work only if all 4 components dont work.

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