Suppose that 8% of a certain batch of calculators have a defective case, and that 11% have defective batteries. Also, 3% have both a defective case and defective batteries. A calculator is selected from the batch at random. Find the probability that the calculator has a good case and good batteries.
To find the probability that the calculator has a good case and good batteries, we need to subtract the probability of having a defective case or defective batteries from 1.
Let's break down the information given:
- 8% of calculators have a defective case (0.08 probability).
- 11% of calculators have defective batteries (0.11 probability).
- 3% of calculators have both a defective case and defective batteries (0.03 probability).
First, let's find the probability of having a defective case or defective batteries:
- Probability of having a defective case = 0.08.
- Probability of having defective batteries = 0.11.
- However, since 3% have both, we need to subtract the probability of having both defects to avoid double-counting: 0.08 + 0.11 - 0.03 = 0.16.
Now, let's find the probability of having a good case and good batteries:
- Probability of having a good case and good batteries = 1 - Probability of having a defective case or defective batteries.
- Probability of having a good case and good batteries = 1 - 0.16 = 0.84.
Therefore, the probability that a calculator selected from the batch has a good case and good batteries is 0.84 or 84%.