# probability

A plane goes missing. According to air trac control, the probability that it has gone
missing in region A is 0.2 and in region B is 0.6. From knowledge of these regions, it is
known that if a plane goes missing in region A, the probability that it will be found is 0.7,
while if a plane goes missing in region B, the probability of it being found is 0.6.
Using probability notation, answer the following questions.
(a) What is the probability that the plane did not go down in either region A or B? Justify
(b) If the probability of the plane being found if it goes down outside regions A or B is
0.1, what is the total probability of the plane not being found at all?
(c) If the plane isn’t found, what is the probability it went down in region A?
(d) If two planes go missing independently, what is the probability that they are both
found?
Question 2 10 marks
An engineer submits 3 proposals to the Council to develop renewable energy supply to a
number of manufacturing plants. From past experience, the chance of any one proposal
being approved is thought to be 0.65. Let X be the number of projects approved by the
council.
(a) Determine the distribution of the random variable X, and write down the pmf with
the correct parameters.
(b) What assumption are you making about the project approvals, and is this valid?
(c) What is the probability that the engineer gets at least one project approved?
(d) The engineer wants to ensure that at least one project is approved with at least 99%
probability. How many proposals should the engineer submit to ensure this?

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