Two firms V and W consider bidding on a road-building job, which may o

Maggenifh

Maggenifh

Answered question

2021-11-14

Two firms V and W consider bidding on a road-building job, which may or may not be awarded depending on the amounts of the bids. Firm V submits a bid and the probability is 0.8 that it will get the job provided firm W does not bid. The probability is 0.7 that W will be bid, and if it does, the probability that V will get the job is only 0.4
a) What is the probability that V will get the job?
b) If V gets the job, what is the probability that W did not bid?

Answer & Explanation

Howell

Howell

Beginner2021-11-15Added 11 answers

Step 1
Given
V=Firm V get job
W=Firm W does bid
Wc=Firm W does not bid
Firm V submits a bid and the probability is 0.8 , that it will get job provided firm W does not bid.
P(VWc)=0.8
The probability that W will bid is 0.7. That is
P(W)=0.7
Therefore P(Wc)=1P(W)=10.7=0.3
The probability that V will get the job given that W will bid is 0.4. That is
P(VW)=0.4
Step 2
a) We want to find the probability that V will get the job.
By using total probability theorem,
P(V)=P(VW)×P(W)+P(VWc)×P(Wc)
=0.4×0.7+0.8×0.3
=0.52
The probability that V will get the job is equal to 0.52
Step 3
b) We want to find conditional probability of Wc given V.
P(WcV)=1P(WV)
Now, first find P(WV)
P(VW)=P(VW)P(W) (by using conditional probability rule)
P(VW)=P(VW)×P(W)
=0.4×0.7
=0.28
Therefore
P(WV)=P(VW)P(V)
=0.280.52
=0.5385
Step 4
Therefore
P(WcV)=1P(WV)
=10.5385
=0.4615
If V gets the job, the probability that W did not not bid is equal to 0.4615

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