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?

  • $\begingroup$ This should be conditional probability. I seem to get 2/5 instead. $\endgroup$ – Hesky Cee Feb 14 '14 at 0:52

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 $1/2 * 2/5 = 1/5$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.