Bloom asked in Science & MathematicsMathematics · 6 months ago

A foreman for an injection-molding firm admits that on 55% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 3% to 15%. The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night?

Relevance
• Pope
Lv 7
6 months ago

This one keeps coming up. I like the problem, but I can never seem to persuade anyone. Let me show it once more. Below are two event definitions.

F: The foreman forgets to shut of the machine.

D: The selected molding is defective.

These conditions are given:

P(F) = 0.55

P(D | F') = 0.03

P(D | F) = 0.15

What you want is P(F | D).

P(F ∩ D)

= P(F) P(D | F)

= (0.55)(0.15)

= 0.0825

P(F' ∩ D)= P(F') P(D | F')= (1 - 0.55)(0.03)= 0.0135

P(D)

= P(F ∩ D) + P(F' ∩ D)

= 0.0825 + 0.0135

= 0.096

P(F | D)

= P(F ∩ D) / P(D)

= 0.0825 / 0.096

= 0.859375

≈ 86%

• 6 months ago

The probability of a defective molding after a shut-off = .03

The probability of a defective molding after not shut-off = .15

A defective molding is five times more probable if the machine overheats.

5 + 1 = 6.  100% ÷ 6 × 5 = 83.3%

Probability the machine was not shut off = 0.83333…

Still have questions? Get answers by asking now.