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## Homework Statement

A factory makes glass bottles, and 15.0% of the bottles are considered defective. A defective bottle will break 60.0% of the time when dropped from a controlled height, whereas a non-defective bottle will only break 10.0% of the time in the same conditions.

You pick a single bottle at random and drop it four times in a row. It doesn't break. What is the probability that it is a defective bottle?

## Homework Equations

## The Attempt at a Solution

If a defective bottle breaks 60% of the time, I calculated the probability of it surviving four consecutive drops: (1-0.60)

^{4}= 0.0256 (2.56%)

This is where I get doubtful, I'd tend to say that if 20% of the bottles are defective, and we picked a single bottle at random, that the probability that the bottle is defective would be:

0.0256 * 0.20 = 0.00512 (0.512%)

Not the right answer. Also, I feel that the last step was incorrect.

Any help would be greatly appreaciated!

Marc