Question

Defective Merchandise 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.

Answer 1

Answer:

0.84 = 84% probability that the calculator has a good case and good batteries.

Step-by-step explanation:

We have these following percentages:

8% of a certain batch of calculators have a defective case.

11 % have defective batteries.

3% have both a defective case and defective batteries.

Using Venn Diagrams:

Event A: Defective Case

Event B: Defecitve Battery

So the probabilities are: $P(A) = 0.08, P(B) = 0.11, P(A \cap B) = 0.03$

Probability of at least one problem:

$P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.08 + 0.11 - 0.03 = 0.16$

Find the probability that the calculator has a good case and good batteries.

No problems, so

$p = 1 - P(A \cup B) = 1 - 0.16 = 0.84$

0.84 = 84% probability that the calculator has a good case and good batteries.