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?

Question

Mathematics

Eduardo Shepherd

7 August, 12:22

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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Answers (1)

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Cade Hogan · Answer 1

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.