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Forikh
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Company provides plumbing and heating contracts. Marketing 20 Aug 2006, 12:34
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Company provides plumbing and heating contracts. Marketing dept figured that company had about a 50% chance of winning the plumbing contract, about 45% chance of winning the heating contract and about 15% winning both.
1.What's probability that they win at least one contract?
2. what is probability that they win exactly one contract?
3. given taht they win the plumbing contract, what is the probability that they win the heating contract/

please give as deatiled explanantion as possible.
Thanks



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Company provides plumbing and heating contracts. Marketing 20 Aug 2006, 14:49
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Forikh
Company provides plumbing and heating contracts. Marketing dept figured that company had about a 50% chance of winning the plumbing contract, about 45% chance of winning the heating contract and about 15% winning both.
1.What's probability that they win at least one contract?
2. what is probability that they win exactly one contract?
3. given taht they win the plumbing contract, what is the probability that they win the heating contract/

please give as deatiled explanantion as possible.
Thanks
Show more


Denote: Plumbing as L and Heating as H, negation as ~P and ~H

Thus we have:
P(L) = 0.5
P(H) = 0.45
P(HL) = 0.15

For 1: P(no contracts) = 1 - P(HL) = 0.85
P(atleast 1 contract) = P(H) + P(L) - P(none) = 0.5 + 0.45 - 0.85 = 10%

For 2: P(only 1 contract) which is either heating or plumbing but not both
= P(H) + P(L) - P(HL)
= 0.5 + 0.45 - 0.15
= 0.8 or 80%
For 3: Given they one plumbing contract, what is the chance of winning heating contract

now: P(HL) = P(L).P(H/L)
Since we already have: P(HL) = 0.15 and P(L) = 0.5

therefore: P(H/L) = 0.15/0.5 = 0.30 or 30%
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Company provides plumbing and heating contracts. Marketing 20 Aug 2006, 15:34
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Forikh
Company provides plumbing and heating contracts. Marketing dept figured that company had about a 50% chance of winning the plumbing contract, about 45% chance of winning the heating contract and about 15% winning both.
1.What's probability that they win at least one contract?
2. what is probability that they win exactly one contract?
3. given taht they win the plumbing contract, what is the probability that they win the heating contract/

please give as deatiled explanantion as possible.
Thanks
Show more


Denote: Plumbing as L and Heating as H, negation as ~P and ~H

Thus we have:
P(L) = 0.5
P(H) = 0.45
P(HL) = 0.15

For 1: P(no contracts) = 1 - P(HL) = 0.85
P(atleast 1 contract) = P(H) + P(L) - P(none) = 0.5 + 0.45 - 0.85 = 10%

For 2: P(only 1 contract) which is either heating or plumbing but not both
= P(H) + P(L) - P(HL)
= 0.5 + 0.45 - 0.15
= 0.8 or 80%
For 3: Given they one plumbing contract, what is the chance of winning heating contract

now: P(HL) = P(L).P(H/L)
Since we already have: P(HL) = 0.15 and P(L) = 0.5

therefore: P(H/L) = 0.15/0.5 = 0.30 or 30%
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Company provides plumbing and heating contracts. Marketing Updated on: 23 Aug 2006, 22:58
Originally posted by ps_dahiya on 20 Aug 2006, 16:57.
Last edited by ps_dahiya on 23 Aug 2006, 22:58, edited 1 time in total.
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Make a Venn diagram:

H = 0.50
L = 0.45
HL = 0.15
Only H = 0.5-0.15 = 0.35
Only L = 0.45-0.15 = 0.30
Neither H nor L = 1-(0.5+0.45-0.15) = 0.20

I: Atleast one = 1-None = 1-0.20 = 0.8
II: 0.35+0.30 = 0.65
III: 0.15/0.5 = 0.3
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Company provides plumbing and heating contracts. Marketing 23 Aug 2006, 20:14
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ps_dahiya
Make a Venn diagram:

H = 0.50
L = 0.45
HL = 0.15
Only H = 0.5-0.15 = 0.35
Only L = 0.45-0.15 = 0.30
Neither H nor L = 0.5+0.45-0.15 = 0.80

I: Atleast one = 1-None = 1-0.80 = 0.2
II: 0.35+0.30 = 0.65
III: 0.15/0.5 = 0.3
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Hi PS_DAHIYA...

why not this:

Part I: At least one contract.
P(H or L, or both)= P(H) + P(L) - P(H y L) = 0.5 + 0.45 - 0.15 = 0.8

Part II: win exactly one contract:
P(H or L, no both) = P(H or L, or both) - P(H y L) = 0.8 - 0.15 = 0.65


.
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ps_dahiya
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Company provides plumbing and heating contracts. Marketing 23 Aug 2006, 22:57
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zorro13
ps_dahiya
Make a Venn diagram:

H = 0.50
L = 0.45
HL = 0.15
Only H = 0.5-0.15 = 0.35
Only L = 0.45-0.15 = 0.30
Neither H nor L = 0.5+0.45-0.15 = 0.80

I: Atleast one = 1-None = 1-0.80 = 0.2
II: 0.35+0.30 = 0.65
III: 0.15/0.5 = 0.3

Hi PS_DAHIYA...

why not this:

Part I: At least one contract.
P(H or L, or both)= P(H) + P(L) - P(H y L) = 0.5 + 0.45 - 0.15 = 0.8

Part II: win exactly one contract:
P(H or L, no both) = P(H or L, or both) - P(H y L) = 0.8 - 0.15 = 0.65


.
Show more

My bad...
corrected that.



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