Johnson has a corporate proposal. The probability that vice-president

Question

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. 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

Kudos for a correct solution.

A. 0.12 
B. 0.24 
C. 0.28 
D. 0.48 
E. 0.72

adityadon · Accepted Answer

Is answer E ? 0.72 
It can be solved as 
(1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )

=0.6*0.2+0.4*0.3+0.6*0.8
= 0.12+0.12+0.48
=0.72

KarishmaB · Answer

P (Atleast one VP approves) = 1 - P(Both VPs disapprove) = 1 - (0.4*0.7) = 0.72

Answer (E)

Note how you get 0.4*0.7. The probability that Adams disapproves = 0.4. 
If Adams disapproves, the probability that Baker approves is 0.3 so the probability that Bakers disapproves = 0.7

EMPOWERgmatRichC · Answer

Hi adityadon,

I like your approach - it has the benefit of being logical AND correct. There is a way to save a bit of work though:

Since the question asks for the probability of AT LEAST one of the VPs approving the proposal, IF Adams approves, then Baker will approve OR disapprove. The 'second part' of that calculation does not need to be separated into two possibilities -it can be done in one step.

(Adams approves) = .6
(Baker approves OR disapproves) = 1
(.6)(1) = .6

Then you just have to consider what happens if Adams DISAPPROVES....

(Adams disapproves) = .4
(Baker approves) = .3
(.4)(.3) = .12

Total probability of at least one approving = .6 + .12 = .72

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

shriramvelamuri · Answer

Dear EmpowerGmatRich,

Please could you help me with this question. I already knew solution for this problem, but was confused because by the wording in the question.

My confusion arises from 1. If Adam approves, then probability of Baker approving is....

and 2. If Adam disapproves, then

Isnt it that the probabality of one event happening is dependent on another event happening. The question seemed not straight forward here and I was confused.

EMPOWERgmatRichC · Answer

Hi shriramvelamuri,

Yes, in this question the probability of the first event effects the second event. This is called 'conditional probability.'

The question asks for the overall probability of AT LEAST one (or the two people) supporting the proposal. In one of the earlier posts, adityadon properly broke this down into 3 possible ways that end in a 'successful' result:

1) Adams approves and Baker does
2) Adams approves and Baker does NOT
3) Adams disapproves and Baker approves

The only outcome that does not end in 'success' is if BOTH Adams and Baker DISAPPROVE.

So, you can either calculate the 3 events that end with at least one approval OR you can calculate the 1 event that ends in 0 approvals (and subtract that result from 1).

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

Here, the combinations (A and not B), (not A and B), and (A and B) all lead to approval of the proposal. The only one that doesn’t is the complement (not A and not B).

P(not A and not B) = P(not A)*P(not B|not A) = (0.4)*(0.7) = 0.28

P(at least one) = 1 – P(not A and not B) = 1 – 0.28 = 0.72

Answer = (E)

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/johnson-has- ... 94287.html https://gmatclub.com/forum/johnson-has- ... 38926.html https://gmatclub.com/forum/johnson-has- ... 38925.html

josearchila86 · Answer

-Since it says "At least", then it is easier to use the strategy "1 minus contrary probability", the contrary probability in this case is that neither of both approve.
-Now we have to look for the probability that both DONT approve and substract it from 1.

Probability that Adams approves: 0.6
 Probability that Adams does not approve: 0.4  WE NEED THIS ONE!!

Probability that Baker approves IF ADAMS APPROVES: 0.8
Probability that Baker APPROVES IF ADAMS DOES NOT APPROVE: 03 --------------- THEN THE PROBABILITY THAT  BAJKER DOES NOT APPROVE IF ADAMS DOES NOT APPROVE IS 0,7  THATS THE OTHER ONE WE NEED!

Multiply both 0.7*0.4 = 0.28 
 
Then 1- 0.28= 0.72 ANSWER IS (E)

bumpbot · Answer

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Johnson has a corporate proposal. The probability that vice-president

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Johnson has a corporate proposal. The probability that vice-president

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615 to 715 in 15 Days (Ria's Strategies)

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