Betting on Horse Races

$P$ makes a bet with $Q$ of $\pounds 8$ to $\pounds 120$ that three races will be won by the three horses $A$, $B$, $C$, against which the betting is $3$ to $2$, $4$ to $1$, and $2$ to $1$ respectively. The first race having been won by $A$, and it being known that the second race was won either by $B$, or by a horse $D$ against which the betting was $2$ to $1$, find the value of $P$'s expectation.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXXII. Probability, Examples XXXII.d, No. 15