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missyli400
28.05.2020 •
Mathematics
When a machine is adjusted properly, 50% of the items it produces are good and 50% are bad. However, the machine is improperly adjusted 10% of the time; in this case, 25% of the items it makes are good and 75% are bad. Suppose that 5 items produced by the machine are selected at random and inspected. If 4 of these items are good (and 1 is bad), what's the probability that the machine was adjusted properly at the time?
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Ответ:
Step-by-step explanation:
Probability of good given properly adjusted P(G/P) = .5
Probability of bad given properly adjusted P(B/P) = .5
Probability of inappropriately adjusted P(I ) = .1
Probability of properly adjusted P(P) = .4
Probability of good given inappropriately adjusted P( G/I ) = .25
Probability of bad given inappropriately adjusted P(B/I ) = .75
P( G ) = P(G/P) x P(P) + P( G/I ) x P(I )
P(P/G) = P(G/P) x P(P) / P(G/P) x P(P) + P( G/I ) x P(I )
= .5 x .4 / .5 x .4 + .25 x .1
= .20 / .20 + .025
.20 / .225
20 / 22.5
= 4 / 4.5 .
= 8 / 9 .
Ответ: