A manufacturer of tablets receives its LED screens from three different supplier

Question

A manufacturer of tablets receives its LED screens from three different suppliers, 70% from B1, 20% form B2 and 10% from B3. In other words, the probabilities that any one LED screen received by the plant comes from these three supplies are 0.7, 0.2, and 0,1. Also, 90% of the LED screens from B1, 85% of those from B2, and 60% of those from B3 perform according to specifications.

(a) What its the probalility that randomly selected LED screen received by the plant performs according ti the specifications?

(b) What is the probalility that a randomly selected LED screen is from B1 if the screen performs according to specifcations?

Explanation / Answer

P(B1) = 0.7

P(B2) = 0.2

P(B3) = 0.1

P(according to specifications | B1) = 0.9

P(according to specifications | B2) = 0.85

P(according to specifications | B3) = 0.6

a) P(according to specifications) = P(according to specifications | B1) * P(B1) + P(according to specifications | B2) * P(B2) + P(according to specifications | B3) * P(B3)

                                                    = 0.9 * 0.7 + 0.85 * 0.2 + 0.6 * 0.1

                                                    = 0.86

b) P(B1 | according to specifications) = P(according to specifications | B1) * P(B1) / P(according to specifications)

                                                           = 0.9 * 0.7 / 0.86

                                                           = 0.733

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