An automated production line produces batteries; the probability of a finished battery being defective is 0.02. Before packaging, the battery is run through a quality control system. The chance of the system detecting a defective battery is 0.99. The probability of throwing a working battery in the trash is 0.01. Find the probability that a randomly selected battery will be defective.
Answer to the problem and its solution
There can be 2 outcomes:
- The battery is broken and the system is not letting it through.
- The power supply is intact, but the system is rejecting it.
The probability of the first case is P1=0.02*0.99
The probability of the 2nd outcome is P2=(1-0.02)*0.01
As a result, the desired chance will be found as follows:
P=P1+P2=0.02*0.99+0.98*0.01
P=0.0198+0.0098=0.0296
As a result, the probability is equal to 0.0296
Solving the problem on video
This video explains in detail how to solve this problem using different methods. So, if you have time, we recommend watching it. The YouTube video is 6 minutes long. If you're short on time, simply use the solution described above.
There are several similar problems, but the principle is the same: you just need to substitute numbers.
