compute the expected cost when each plan is used for treatment?

Question

Antiboitic A effectively cures the infection 60% of the time & costs 50$.
Antibiotic B effectively cures the infection 90% of the time & costs 80$.
Plan 1: Treat with antibiotic A first and if it isnt effective then treat with antiobiotic B
Plan 2: Treat with antibiotic B first and if it isnt effective then treat with antibiotic A
Both antibiotics work independently of eachother

Answer 1

Plan 1: 50 + 0.4 * 80 = 82
Plan 2: 80 + 0.1 * 50 = 85

Answer 2

Plan 1:
$50+.4*$80=$50+$32=$82

Plan 2:
$80+.2*$50=$80+$10=$80

Answer 3

P(A)=0.5, P(B) = 0.9, P(~A) = 1-P(A), P(~B)=1-P(B).
P(A&~B) = P(A)*P(~B), P(B&~A) = P(B)*P(~A)

E[p1] = P(A)*$50 + P(B&~A)*($50+$80)

E[p2] = P(B)*$80 + P(A&~B)*($50+$80)