As part of a game show a player spins a wheel with 18 slots, 12 marked "OK, Stop!" and 6 marked "Go On...". The player spins no more than 4 times. On each spin, if the wheel stops at "OK, Stop!" , the player wins a prize and stops; the prize on spin 1 is $100. If the spin is "Go On,..." on spins 1 through 3 the prize is multiplied by 10 and the player spins again; if spin 4 is "Go On,..." the player wins the grand prize of $1,000,000.

In the questions below, let the variable YYbe the number of spins and the variable XXbe the dollars won.

Find an expresion for the probability distribution of the number of spins YY, p(y)p(y).

Find the value of p(y)p(y)for each value of yyand calculate the mean number of spins E(Y)E(Y).

If spins could continue without limit until "OK, Stop!" comes up (once), what would be the expected number of spins?

What is the probability that the player wins the grand prize of $1,000,000?

Find the mean dollars won for this game, E(X)E(X).