Question

A box contains a large number of batteries. The probability that a battery is faulty is 0.15. How many batteries would you need to select to be more than 95% certain of picking at least one faulty battery?

Answer 1

To be more than 95% certain of picking at least one faulty battery, you would need to select approximately 7 batteries.

Step-by-step explanation:

To be more than 95% certain of picking at least one faulty battery, we can use the concept of complement probability. The probability of not picking any faulty battery in one selection is 1 - 0.15 = 0.85. Let's denote this probability as p.

To find the number of batteries needed to be more than 95% certain, we need to find the smallest number of selections where the probability of not picking any faulty battery in all selections is less than 0.05. This can be calculated using the formula:

p*x < 0.05

where p is the probability of not picking a faulty battery in one selection and x is the number of selections. By solving this equation, we can find that approximately 7 batteries need to be selected.