Bunuel
Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
A. 0.14
B. 0.26
C. 0.49
D. 0.55
E. 0.86
Kudos for a correct solution.
MAGOOSH OFFICIAL SOLUTION:We will use the abbreviation A = VP Adams approves, B = VP Baker approves, and C = VP Corfu approves.
P(funding) = P(A and (B or C)) = P(A)*P(B or C)
We can multiply because everything is independent of everything else. First look at P(B or C). These are not mutually exclusive, so we need to use the generalized
OR rule:
P(B or C) = P(B) + P(C) – P(B and C)
Because B & C are independent, we can multiply to find P(A and B)
P(B or C) = (0.5) + (0.4) – (0.5)*(0.4) = 0.9 – 0.2 = 0.7
Now, multiply by P(A)
P(funding) = P(A)*P(B or C) = (0.7)*(0.7) = 0.49
Answer = (C)