Machine set up is correct 60% of time & is incorrect 40% of time, 10 % of parts produced are defective when set up is correct, & 60 % would be defective if set up is incorrect. Find the probability that part is defective even though machine was set up correctly
To find the probability that a part is defective even though the machine was set up correctly, we can use Bayes' theorem.
Let's denote the event of the machine being set up correctly as A and the event of a part being defective as B. We want to calculate P(B|A), which represents the probability of B occurring given that A has occurred.
Let's break down the information given:
P(A) = 60% = 0.6 (probability of the machine being set up correctly)
P(not A) = 40% = 0.4 (probability of the machine being set up incorrectly)
P(B|A) = 10% = 0.1 (probability of a part being defective when the machine is set up correctly)
P(B|not A) = 60% = 0.6 (probability of a part being defective when the machine is set up incorrectly)
We can calculate P(B) by considering the Law of Total Probability:
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
Plugging in the values:
P(B) = (0.1 * 0.6) + (0.6 * 0.4)
= 0.06 + 0.24
= 0.3
Therefore, the probability that a part is defective even though the machine was set up correctly is 0.3 or 30%.