Question

Suppose that 1010​% of a certain batch of calculators have a defective​ case, and that 1414​% have defective batteries.​ Also, 55​% 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: Our required probability is 81%.

Explanation:

Since we have given that

Probability of defective calculators (C)= 10%

Probability of defective batteries (B) = 14%

Probability of both defective calculators and defective batteries = 5%

So, it becomes.

`P(C\cup B)=P(C)+P(B)-P(B\cap C)\\\\P(C\cup B)=10+14-5\\\\P(C\cup B)=19\%`

So, probability that the calculator has a good case and good batteries is given by

`100\%-19\%=81\%`

Hence, our required probability is 81%.