Bayes theorem in odds form - incorrect in Tetlock's 'Superforecasting' book?

Page 170 in Philip Tetlock's et al. Superforecasting book shows Bayes' theorem in odds form as:

$$\frac{P (H|D)}{P (\neg H|D)} = P (D|H) P (D|\neg H) \frac{ P (H)}{P (\neg H)}$$

Posterior Odds = Likelihood Ratio • Prior Odds

Shouldn't the Likelihood Ratio be $\frac{P (D|H)}{P (D|\neg H)}$, i.e. division instead of multiplication?

• Quite right: this is a typo. – Xi'an Nov 26 '15 at 14:02

We know $P(A|B)=\frac{P(B|A)\cdot P(A)}{P(B)}$, so:
$$\frac{P(A|B)}{P(\bar{A}|B)}=\frac{\frac{P(B|A)\cdot P(A)}{P(B)}}{\frac{P(B|\bar{A})\cdot P(\bar{A})}{P(B)}}$$
$$=\frac{P(B|A)\cdot P(A)}{{P(B|\bar{A})\cdot P(\bar{A})}}$$
$$=\frac{P(B|A)}{{P(B|\bar{A})}}\cdot \frac{P(A)}{P(\bar{A})}$$