Probability Watch

mrboomtastic1
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You have decided to bid for the contract to run a fitness centre. Three other bodies are likely to bid also, but you will not know they do so or not. The probability that A bids is 0.5, the probability that B bids is 0.75, and the probability that C bids is 0.5

a) what is the probability that only you bid?
b) what is the probability that everyone bids?
c) what is the probability that only you and A bids?
d) what is the probability that only you and B bids?
e) what is the probability that only you and C bids?


Thank you for your help.
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ttoby
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We can assume that A, B and C don't know about each other's bids so they're all independent.

a) That's P((not A) and (not B) and (not C)) = P(not A)*P(not B)*P(not C)

b) P(A and B and C)

c) P(A and (not B) and (not C))

d) and e) are similar questions to c).
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jndk109
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(Original post by ttoby)
We can assume that A, B and C don't know about each other's bids so they're all independent.

a) That's P((not A) and (not B) and (not C)) = P(not A)*P(not B)*P(not C)

b) P(A and B and C)

c) P(A and (not B) and (not C))

d) and e) are similar questions to c).
theres four bids buddy your bid and three others
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ttoby
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(Original post by jndk109)
theres four bids buddy your bid and three others
We're told that you are definitely bidding. This means that the probabilities are equivalent to:

a) P(none of A, B or C bid)
b) P(A, B and C all bid)
c) P(A bids but B and C don't bid)

etc
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jndk109
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(Original post by ttoby)
We're told that you are definitely bidding. This means that the probabilities are equivalent to:

a) P(none of A, B or C bid)
b) P(A, B and C all bid)
c) P(A bids but B and C don't bid)

etc
good point your right
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mrboomtastic1
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(Original post by ttoby)
We're told that you are definitely bidding. This means that the probabilities are equivalent to:

a) P(none of A, B or C bid)
b) P(A, B and C all bid)
c) P(A bids but B and C don't bid)

etc

Thanks.
Also:
You feel that, irrespective of how many organisations bid, each of the other organisations has an equal chance of winning the contract(provided it bids) and you have twice as good a chance as each other organisation of winning the contract. What is the probability that you win the contract?

Thank you for the help.
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ttoby
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(Original post by mrboomtastic1)
Thanks.
Also:
You feel that, irrespective of how many organisations bid, each of the other organisations has an equal chance of winning the contract(provided it bids) and you have twice as good a chance as each other organisation of winning the contract. What is the probability that you win the contract?

Thank you for the help.
P(I win)
= P(I win | none of A, B, C bids)*P(none of A, B, C bids)
+ P(I win | 1 of A, B, C bids)*P(1 of A, B, C bids)
+ P(I win | 2 of A, B, C bids)*P(2 of A, B, C bids)
+ P(I win | all of A, B, C bids)*P(all of A, B, C bids)

= 1*a + (2/3)*(c+d+e) + (1/2)*P(2 of A, B, C bids) + (2/5)*b

Where a, b, c, d and e are your answers to those questions.

Therefore, to answer this question you need to calculate P(2 of A, B, C bids) in a similar way to how you did questions c-e then work out the probability of winning as above.
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mrboomtastic1
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(Original post by ttoby)
P(I win)
= P(I win | none of A, B, C bids)*P(none of A, B, C bids)
+ P(I win | 1 of A, B, C bids)*P(1 of A, B, C bids)
+ P(I win | 2 of A, B, C bids)*P(2 of A, B, C bids)
+ P(I win | all of A, B, C bids)*P(all of A, B, C bids)

= 1*a + (2/3)*(c+d+e) + (1/2)*P(2 of A, B, C bids) + (2/5)*b

Where a, b, c, d and e are your answers to those questions.

Therefore, to answer this question you need to calculate P(2 of A, B, C bids) in a similar way to how you did questions c-e then work out the probability of winning as above.
Thank you very much.
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