When a machine is working properly only 4% of the units it produces are defective.When it slips out of adjustment, the rate jumps to 25% and the machine has to be shut down and adjusted.On 90% of the mornings when production restarts, the machine is in proper adjustment.You turn on the machine this morning and produce the first unit.How likely is it that the first unit is defective?
A).057
B).061
C).10
D).126
E).04

Question

Quizplus · Accepted Answer

To find the probability that the first unit is defective, we need to consider both scenarios: when the machine is working properly and when it is not. The probability of the machine being in proper adjustment is 90%, and in this case, the probability of producing a defective unit is 4%. The probability of the machine being out of adjustment is 10%, with a 25% chance of producing a defective unit. Thus, the total probability of a defective unit is (0.9 * 0.04) + (0.1 * 0.25) = 0.036 + 0.025 = 0.061.

When a Machine Is Working Properly Only 4% of the Units