Take the 2-minute tour ×  Let's say I have a factory producing
28% defective bottles. A defective bottle has a 66.5% chance of
breaking when dropped on the ground and a non-defective bottle
only has a 9.5% chance to break.  Given that I dropped a
randomly picked bottle on the ground 4 times and it didn't break
(its chance to break doesn't increase with every drop), what is
the chance for that bottle to be defective?  This is a homework
question and I attempted to use Bayes' rule such as  $
P(Defective | IntactX4) =
{P(IntactX4|Defective)P(Defective)\over P(IntactX4)} $  $
P(Defective | IntactX4) = {(1-0.665)^4 * 0.28\over
(0.28*(1-0.665)+(1-0.28)*(1-0.095))^4} $   $ P(Defective |
IntactX4) \approx0.011422987612 $  However, this does not appear
to be the correct answer. I wonder if there is something wrong
with the way I use Bayes' rule. Can anyone shed some light?
share|improve this question There is a typo (or error) in the
denominator. The first term should be exactly like the
numerator. You are missing an