Johnson has a corporate proposal. The probability that vice

[Mike@Magoosh]

The following information accompanies questions 6-7

Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.8. If VP Adams doesn't approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3.

6) What is the probability that one of the two VPs, but not the other, approves Johnson's proposal?
(A) 0.12
(B) 0.24
(C) 0.28
(D) 0.48
(E) 0.72

7) What is the probability that at least one of the two VPs, approves Johnson's proposal?
(A) 0.12
(B) 0.24
(C) 0.28
(D) 0.48
(E) 0.72

These two questions are paired to raise the subtle question: do they have the same answer? why or why not? How do we calculate them? For a full discussion of tricky probability questions, as well as the OA & OE for these, see:
https://magoosh.com/gmat/2014/gmat-advan ... -problems/

Mike

[Milovan]

Firstly I would create a little recap of the info we have:

P (Adams approves) = 0.6 -> P (Baker approves) = 0.8
P (Baker reject) = 0.2

P (Adams reject) = 0.4 -> P (Baker approves) = 0.3
P (Baker rejects) = 0.7

6) We have two combinations: 1. Adams approves and Baker rejects
2. Adams rejects and Baker approves

P (1. or 2.) = P(1.) + P(2.) - each P(1.) and P(2.) has two dependent cases (approves - rejects and rejects - approves) so we use multiplication between them.

P (1. or 2.) = 0,6 * 0,2 + 0,4 * 0,3 = 0,24 and the answer is B


7) As soon as we see At least we should think about P(good) = 1 - P(bad)
P (at least one approval) = 1 - P(both reject) = 1 - 0,4 * 0,7 = 0,72

The correct answer is E