In November 2024
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Question 1.2 [2, 2, 2]
Suppose that we have two events A and B such that P A( ) 0.8 = and P B( ) 0.7 = .
a) Is it possible that PA B ( ) 0.1 ∩ = ? Explain your answer.
b) What is the smallest possible value of PA B ( ) ∩ ?
c) What is the largest possible value of PA B ( ) ∩ ?
Question 1.1 [2, 2, 2, 2, 2]
A local farmer plants a given number carrots on a certain number of days. We are looking at the
number of carrots the farmer can plant over two days. Suppose that the famers must plant at least
4 carrots on the first day, no more than 9 carrots on the second day and farmer has to plant more
carrots on the second day than the first day.
a) Determine the sample space of the experiment.
b) If each of the outcomes in (a) have equal probability of occurring find the probability of the
following events:
i. Event that there were 13 carrots in total planted over the two days.
ii. Event that an odd number of carrots were planted on the second day.
c) Are the events (i) and (ii) mutually exclusive? Motivate your answer!
d) Are the events (i) and (ii) statistically independent? Motivate your answer!
Question 2.8 [2, 3, 3]
Suppose that a telemarketer has a 12% chance of making a sale on any given call. If the
telemarketer makes average of 5 calls per hour, calculate:
a) The probability that the telemarketer will make exactly 2 sales during the shift.
b) The probability that the telemarketer will makes more than 4 sales during the shift.
c) What is the probability that the telemarketer makes more than 2 call during two hours?
Question 2.8 [2, 3, 3]
Suppose that a telemarketer has a 12% chance of making a sale on any given call. If the
telemarketer makes average of 5 calls per hour, calculate:
a) The probability that the telemarketer will make exactly 2 sales during the shift.
b) The probability that the telemarketer will makes more than 4 sales during the shift.
c) What is the probability that the telemarketer makes more than 2 call during two hours?
Question 2.6 [3, 3, 3]
Suppose that the height of seven-year old children is a normal random variable with mean 1.1m and
standard deviation 0.1m.
a) What proportion of seven-year old children are shorter than 0.95m?
b) What is the probability that a seven-year old child is taller than 1m but shorter than 1.175m?
c) Suppose that a family restaurant has a children’s play-place. The facilities in the play-place
can only be used by children below a certain height. What should the cut-off height be to
ensure that 99% of seven-year olds have access to the play-place?
Question 2.4 [3, 2, 1, 2]
Adam is a keen soccer player. One afternoon he decides to practice his kicking skills, and places a
large box 20m away from him. He then kicks the ball at the box and tries to hit it. He decides that he
will only stop once he hits the box ten times. Suppose that the probability of him hitting the box with
any kick is 40%.
a) What is the probability that Adam takes 20 kicks before he can stop?
b) What is the probability that it takes him at least 13 kicks before he can stop?
c) What is the expected value of the number of kicks he will make before he can stop?
d) Based on your answer in (c), would you be surprised if Adam told you it took him 50 kicks
before he hit the box ten times? Why?
Question 2.3 [1, 3, 3, 2, 2, 2]
Dr Clohessy drives to work every day, and she passes 11 traffic lights. If each traffic light works
independently from each other and each have a probability of being green when DR Clohessy drives
up to the light of 0.25. Use this information to answer the following questions.
a) Define the random variable X of the experiment.
b) What is the probability that at least two lights will be green on her morning drive through the
11 traffic lights?
c) What is the probability that at least two lights will be green, given that at least one has already
been green?
d) What is the probability that three lights will be red through the 11 traffic lights?
e) Determine the mean of X and standard deviation of X of the number of green traffic lights.
f) Now suppose you are interested in the first traffic light that turns
Suppose the mean number of days to germination of a variety of seeds is 22, with a standard deviation of 2.3 days. Find the probability that the mean germination time of a sample of 160 seeds will be within 0.5 days of the population mean.
3 suppose ‘X’ is normally distributed with mean 20 and variance 8 i.e X-NID
Find
A P(25≤X≤30)
B P(X≥25)
4 Given the following discrete probability destruction.
X 1 5 7 9
F(x) 1/6 2/6 2/6 1/6
Find
A the expected value of x E(X)
The variance of x V(X)
6 the probabilities that Abebe passes microeconomics is 2/3 and the probability that he passed statics 4/9. If the probability of passing both courses is 1/4 ,what is the probability that Abebe will pass at lease one of these courses
workout
1 Assume that each applicant is equally chosen for a job.
Male applicants are 6 black and 14 white, and female applicants are 10 black and 20 white.
Find the probability that an applicant’s chosen a female given that black is chosen
2 a new drug is effective 60% of the time. What is the probability that in a random sample of 4 patients, it will be effective on two of them? Is it binomial or passion justify?
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#339914 on Dec 2023