Help with Statistics Question Watch

MathHead
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Need help with following questions wud really appreciate it.

• The probabilities that three archers Matt, John and Jenny hit a target are 0.7, 0.4 and 0.6 respectively. Each shoots once at the target and their shots are independent.
-Given that only one of them hits the target then that one was Matt.
-Someone sees one of the three archers hit the target without knowing who it was.What is the probability that it was John?

•A truck manufacturer wishes his customers to keep enough petrol in their fuel tanks.The manufacturer wants therefore to set the warning mark so that sufficient fuel remains for there to be only a one in a hundred chance of the driver not reaching the next petrol station.

A truck does 40km to the litre on average. An assumption is made that petrol stations are found along the road according to a Poisson distribution and the mean rate of occurrence is measured as λ = 0.10 petrol stations per km. For a Poisson distribution the probability of no occurrences within a fixed interval of length x is exp(-λx).

(i) Why is exp(-λx) not a probability density?
(ii) How many litres should there be in the fuel tank when the needle is against the warning mark?
(iii) Comment on the suitability of the Poisson distribution for this situation.


if you could provide (take a picture of ur working out on paper) or explain the method it would be very helpful.


thanks
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