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?
- PopeLv 76 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)
P(F' ∩ D)= P(F') P(D | F')= (1 - 0.55)(0.03)= 0.0135
= P(F ∩ D) + P(F' ∩ D)
= 0.0825 + 0.0135
P(F | D)
= P(F ∩ D) / P(D)
= 0.0825 / 0.096
- The GnosticLv 76 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…