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The probability that a contractor will get a plumbing contract is 2/3

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Re: The probability that a contractor will get a plumbing contract is 2/3 [#permalink]
gautamgogoi96 wrote:
The probability that a contractor will get a plumbing contract is 2/3 and the probability that he will get an electric contract is 7/12.If the probability to get
exactly one contract is 5/8,the probability that he does not get any contract is

(A)1/16

(B)1/12

(C)3/32

(D)1/8

(E)1/18

Given: The probability that a contractor will get a plumbing contract is 2/3 and the probability that he will get an electric contract is 7/12.
Asked: If the probability to get exactly one contract is 5/8,the probability that he does not get any contract is

Attachment:

Screenshot 2020-07-12 at 12.00.15 AM.png [ 22.62 KiB | Viewed 5916 times ]

5/8 - y + 5/12 - y = 1/3
2y = 5/8 + 5/12 - 1/3 = 17/24
the probability that he does not get any contract = 5/12 - y = 5/12 - 17/48 = 3/48 = 1/16

IMO A
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Re: The probability that a contractor will get a plumbing contract is 2/3 [#permalink]
CrackVerbalGMAT wrote:
Let Plumbing Contract = A and Electric Contract = B

We are given P(Plumbing) = P(A) = 2/3 and P(Electrical) = P(B) = 7/12

Also the probability of getting exactly 1 contract, i.e either only A or only B = 5/8
i.e P( only A) + P(only B) = 5/8

We need to find the probability of him getting neither contracts

In Set Theory

The universal set value = 1
P(A U B) + P(A U B)' = 1
Therefore P(A U B)' = 1 - P(A U B)

We have:

P(A U B) = P(A) + P(B) - P(A∩B)
Therefore P(A∩B) = P(A) + P(B) - P(A U B) ----- (1)

Also P(A U B) = P(only A) + P(Only B) + P(A∩B) ---- (2)

Putting equation (1) in (2), we get
P(A U B) = P(only A) + P(only B) + P(A) + P(B) - P(A U B)

2 * P(A U B) = [P(only A) + P(only B) + P(A) + P(B)]

P(A U B) =1/2* [P(only A) + P(only B) + P(A) + P(B)]

P(A U B) = 1/2 * (5/8 + 2/3 + 7/12) = 1/2 * (15/24 + 16/24 + 14/24) = 1/2*45/24 = 15/16

Therefore P(A U B)' = 1 - P(A U B) = 1 - 15/16 = 1/16

Option A

Arun Kumar

Dear Sir,

I am not clear what does each sign mean.

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Re: The probability that a contractor will get a plumbing contract is 2/3 [#permalink]
There are essentially a system of equations to solve to get the answer.

x=union of probabilities, ie area of overlap of two sets on a 2-set Venn diagram
n= probability of neither

1 = $$\frac{5}{8}$$ + x + n

1= $$\frac{2}{3}$$ + $$\frac{7}{12}$$ - x + n

Adding these two equations yields: $$\frac{1}{8}$$= 2*n

n=$$\frac{1}{16}$$
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Re: The probability that a contractor will get a plumbing contract is 2/3 [#permalink]
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Re: The probability that a contractor will get a plumbing contract is 2/3 [#permalink]
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