A Ticket Holder's Expectation

There is a raffle with $10$ tickets and two prizes of value $\pounds 5$ and $\pounds 1$ respectively. $A$ holds one ticket and is informed by $B$ that he has won the $\pounds 5$ prize, while $C$ asserts that he has won the $\pounds 1$ prize: what is $A$'s expectation, if the credibility of $B$ is denoted by rac{2}{3}, and that $C$'s by rac{3}{4}?

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXXII. Probability, Examples XXXII.d, No. 13