Math probability question? Please help!?

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?

2 Answers

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.