Probability of rolling odd number greater than 5 on a 10 sided die 
If you have a 10 sided die, what is the probability that you will roll an odd number greater than 5?

I tried to approach this as P(odd)*P(greater than 5). Since the probability of rolling an odd number is (1/2) and the probability of rolling a number greater than 5 is also (1/2) the answer should be (1/4).
However, when listing the possibilities, the only odd numbers greater than 5 are 7 and 9, so this gives a probability of 2/10 = 1/5.
Why is the answer wrong when you multiply the probabilities like I first tried?

It's because the probability that it's odd and the probability that it's greater than 5 are not independent.  You can only multiply those probabilities if they're independent (source).  Here, there are 3 odd numbers not greater than 5, but only 2 odd numbers greater than 5, so there's the dependence.
The probability for dependent events is $P(A) * P(B|A)$.  $P(odd) = 1/2$, and $P(greaterThan5 | isOdd) = 2/5$, because out of the $5$ odd numbers, only $2$ are greater than $5$.  Then $1/2 * 2/5 = 1/5$.
