Question 1196997: a contract company has bid on two contracts. the probability of winning contract A is 0.71. the company wins contracts A , the probability of winning contract B is 0.62. if the contract loses contract A, the probability decreases to 0.33. what is the probability of not winning any contract
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
P(won A) = 0.71
P(lost A) = 1 - P(won A) = 1 - 0.71 = 0.29
P(won B, given lost A) = 0.33
P(lost B, given lost A) = 1-0.33 = 0.67
P(lost A and lost B) = P(lost A)*P(lost B, given lost A)
P(lost A and lost B) = 0.29*0.67
P(lost A and lost B) = 0.1943
Answer: 0.1943
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
A contract company has bid on two contracts. The probability of winning contract A is 0.71.
If the company wins contracts A, the probability of winning contract B is 0.62.
If the company loses contract A, the probability of winning contract B decreases to 0.33.
What is the probability of not winning any contract?
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Step by step.
(a) P(A win) = 0.71 (given).
(b) P(both A and B win) = 0.71*0.62 = 0.4402.
(c) P(B win) = 0.71*0.62 + (1-0.71)*0.33 = 0.5359.
(d) P(A or B win) = P(A win) + P(B win) - P(both A and B win) = 0.71 + 0.5359 - 0.4402 = 0.8057.
(e) P(not winning any contract) = complement of (d) to 1 = 1 - 0.8057 = 0.1943. ANSWER
Solved.
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This solution gives the same answer as @math_tutor2020.
Both solutions are equivalent (both are good), but (naturally) my solution
seems more straightforward and clear to me - it is why I came with it . . .
You may choose any of these two solutions, on your choice.
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