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?