V$3\mathrm{.}0$

$2.$ Everyone's favourite "shady character" has returned to Grey Highlands. This time, he is tucked away in the greenhouse, offering to play a game called "Join the Club".

It costs $$1$ to play.

The dealer lays a card on the table, and leaves it there. Then he lays a second, and then a third, leaving them on the table too.

If the hand contains $1$ Club, they win $$1$

If the hand contains $2$ Clubs, they win $$2$

If the hand contains $3$ Clubs, he cries "BEHOLD!

THE SUIT OF DESTINY!" $...$ and they win $$10$

a$)$ Create a tree diagram to track the probability of each

$(10)$ outcome.

$12$

b$)$ Create a chart of the probability distribution for this game, and determine the expected value

c$)$ If it takes about $10$ seconds to play one game, how much money can the "shady character" expect to walk away with after six hours of play?