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

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Bunuel
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Johnson has a corporate proposal. The probability that vice-president [#permalink] New post  08 Mar 2015, 19:09
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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

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Re: Johnson has a corporate proposal. The probability that vice-president [#permalink] New post  08 Mar 2015, 21:33
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Hi

So in this question the situation is as follows

P of approval for Adam's = (P Johnson approves)*(P Baker approves) + (P Johnson approves)*(P corfu approves)
= (0.7*0.3) + (0.7*0.4) = 0.49
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Re: Johnson has a corporate proposal. The probability that vice-president [#permalink] New post  08 Mar 2015, 22:07
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probability of adams approval = 0.7
baker approval =0.5
corfu approval=0.4

proabability of approval is must adam approval and atleast one approval

= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval

= 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4
=0.14+0.21+0.14
=0.49
so answer C sufficient
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Re: Johnson has a corporate proposal. The probability that vice-president [#permalink] New post  09 Mar 2015, 02:30
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Bunuel wrote:
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.


when you summarize the qn, it is a case of atleast 2 approvals. And the case here is approval of Adam's is mandatory.

So the probability of approval is

=P(Adam, Baker, Cofu) + P(Adam, Baker', Cofu) + P(Adam, Baker, Cofu')

= 0.7*0.5*0.4 + 0.7*0.5*0.4 + 0.7*0.5*0.6

= 0.49

Option C
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Re: Johnson has a corporate proposal. The probability that vice-president [#permalink] New post  15 Mar 2015, 19:33
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Bunuel wrote:
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)
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Re: Johnson has a corporate proposal. The probability that vice-president [#permalink] New post  18 Jun 2016, 04:49
A question,

Here why can't we think P(A)+P(B) or P(A)+P(C) ?

So 35/100+28/100 ?
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Re: Johnson has a corporate proposal. The probability that vice-president [#permalink] New post  10 Nov 2020, 01:51
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Bunuel wrote:
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.


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Re: Johnson has a corporate proposal. The probability that vice-president [#permalink] New post  15 Dec 2020, 02:49
probability that adam approves times 1 minus probability that none of the other two vp's approves.

So, probability that none of the other approves is: (1-0.5) x (1-0.4) = 0.3
1 - that = 0.7 (at least one, or both of them will approve)

0.7x0.7= 0.49 (adam approves, and at least one, or both of them will approve)
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