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?
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!