In a factory, machine A, B and C produce electronic components. Machine A produces 16% of the components, machine B produces 50% while machine C produces the rest. Some of the components are defective. MachineA produces 4% ,machineB 3% and machineC 7% defective components. Find the probability that a randomly selected component is defective.
.16*4% + .50*3% + (1-.16-.50)*7% = 4.52%
Well, let's crunch some numbers here. Since machine A produces 16% of the components and 4% of those are defective, we can say that machine A contributes to 16% × 4% = 0.64% of the total defective components.
Similarly, machine B produces 50% of the components and 3% of those are defective. That means machine B contributes to 50% × 3% = 1.5% of the total defective components.
Finally, machine C produces the remaining 100% - 16% - 50% = 34% of the components. And 7% of those are defective, so machine C contributes to 34% × 7% = 2.38% of the total defective components.
To find the probability that a randomly selected component is defective, we add up the contributions from each machine:
0.64% + 1.5% + 2.38% = 4.52%
So, the probability that a randomly selected component is defective is 4.52%. But hey, with all this talk about defective components, let's hope you don't end up with a glitchy toaster or a smoke alarm that goes off randomly!
To find the probability that a randomly selected component is defective, we need to determine the proportion of defective components produced by each machine and then calculate the weighted average.
Let's calculate the proportion of defective components produced by each machine:
Machine A: 16% * 4% = 0.16 * 0.04 = 0.0064
Machine B: 50% * 3% = 0.50 * 0.03 = 0.015
Machine C: The remaining percentage that Machine C produces is 100% - (16% + 50%) = 34%
34% * 7% = 0.34 * 0.07 = 0.0238
Now, we can calculate the weighted average:
Weighted average = (proportion of defective components from Machine A) + (proportion of defective components from Machine B) + (proportion of defective components from Machine C)
= 0.0064 + 0.015 + 0.0238
= 0.0452
Therefore, the probability that a randomly selected component is defective is 0.0452 or 4.52%.
To find the probability of selecting a defective component, we need to consider the proportion of defective components produced by each machine.
First, let's determine the percentage of components that machine C produces. Since machine A produces 16% and machine B produces 50%, the remaining percentage must be produced by machine C. Thus, machine C produces 100% - (16% + 50%) = 34% of the components.
Next, we need to calculate the percentage of defective components produced by each machine. Machine A produces 4% defective components, machine B produces 3%, and machine C produces 7%.
To find the overall probability of selecting a defective component, we need to take the weighted average of the proportions of defective components from each machine. We multiply each proportion by the percentage of components produced by each machine and then sum them up.
Probability of selecting a defective component = (16% * 4% + 50% * 3% + 34% * 7%)
= (0.16 * 0.04 + 0.50 * 0.03 + 0.34 * 0.07)
= 0.0064 + 0.015 + 0.0238
= 0.0452
Therefore, the probability of randomly selecting a defective component is approximately 0.0452, or 4.52%.