Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am probably misusing Bayes' theorem, but I can't figure out how.

$$P(B|A) = 0.4$$

$$P(B) = 0.1$$

$$P(A) = 0.3$$

$$P(A|B) = \dfrac{0.4 \cdot 0.3}{0.1} = 1.2$$

Since the probability of anything can't be > $1$, I must be wrong somewhere. Please help.

share|cite|improve this question
up vote 8 down vote accepted

It is not possible to have the hypothesized probabilities. $P(B|A)=\frac{P(A\cap B)}{P(A)}\leq\frac{P(B)}{P(A)}=\frac{1}{3}\lt 0.4$.

share|cite|improve this answer
Thank you! I see where I went wrong mathematically, but do you have any suggestions on developing the intuition for this? For the problem that I was solving, I picked the probabilities intuitively. Is there a way to quickly check that the probabilities I picked make sense? (Because they make intuitive sense.) – Alexei Andreev Jun 18 '11 at 19:53
@Alexei: To me, $P(B|A)=\frac{P(A\cap B)}{P(A)}$ and $P(A\cap B)\leq P(B)$ are intuitive, and these are all that is needed to check the plausibility here. You can quickly check that $P(B)\geq P(A)P(B|A)$. But I don't know about developing intuition as it applies to the problem you were trying to solve, because I have no idea what that problem is. – Jonas Meyer Jun 18 '11 at 20:13

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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