Question 1033911
It is given that p(1) = 0.12.  Since p(1 or 2) = 0.45, then by mutual exclusivity, p(2) = 0.33.  Since p(2 or 3) = 0.47, then again by mutual exclusivity p(3) = 0.14.  This gives p(4) = 1 - 0.12 - 0.33 - 0.14 = 0.41.

==> Your expected winning is {{{E(X) = 1*0.12 + 2*0.33 + 3*0.14 + 4*0.41 = 2.84}}}.

Therefore your expected winning is $2.84.