SOLUTION: A construction company has submitted bids on 2 contracts A and B. The company feels that it has a 60% chance of winning contract B. Furthermore, the company believes that it has a

Question 248871: A construction company has submitted bids on 2 contracts A and B. The company feels that it has a 60% chance of winning contract B. Furthermore, the company believes that it has a 70% chance of winning contract A given that it wons contract B, and it has a 40% chance of not winning contract A given that it does not win contact B
Given that the company wins contract A, the probability that it will also win contract B is...
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A construction company has submitted bids on 2 contracts A and B. =====
The company feels that it has a 60% chance of winning contract B.
P(B) = 0.6
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Furthermore, the company believes that it has a 70% chance of winning contract A given that it wons contract B,
P(A|B) = 0.7
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and it has a 40% chance of not winning contract A given that it does not win contact B
P(A'|B')= 0.4
--------
Given that the company wins contract A, the probability that it will also win contract B is...
P(B|A) = P(A and B)/P(A) = [P(A|B)*P(B)]/[P(A|B)+P(A|B')]
= [0.7*0.6]/[0.7+0.6] = 0.42/1.3 = 0.3231
=================================================
Cheers,
Stan H.

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