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Question 1.9 [2, 2, 3]
Chantelle has decided to sell baked biscuits to assist in the payment of her university fees. After
baking for hours and packing packets to sell, she finds that she has 9 biscuits left over. Of these 9
biscuits, 4 are chocolate biscuits, 3 are raisin and 2 are peanut butter. She thinks to herself that she
is going to use these 9 biscuits to assist her with understanding probability. She treats each biscuit
as being slightly different, however order of her selection is not important.
Suppose Chantelle selects 3 biscuits at random from the 9, help her answer the following questions:
a) Calculate the probability that of the 3 biscuits randomly selected, 1 is chocolate, 1 is raisin
and 1 is peanut butter.
b) Calculate the probability that only chocolate biscuits are selected
c) Calculate the probability that at least
Question 1.7 [2, 2, 2, 2]
If A and B are independent events with P A( ) 0.52 = and P B( ) 0.21 = , find the following:
a) PA B ( ) ∪
b) PA B ( ) ∩
c) PA B ( ) ∪
d) Are A and B disjoint events? Motivate your answer!
Question 1.8 [3]
A certain washing machine factory has found that 15% of its washing machines manufactured in the
factory break down and are returned in the first year of operation. Suppose that 32 machines are
purchased by a laundromat from this washing machine factory, find the probability that at least one
washing machine breaks down in the first year of operation?
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 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?
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
2. How many 4 letter words can be created, if repetitions are allowed?
3. How many three digit numbers can be formed?
4. How many words (of any number of letters) can be formed from GAME?
5. How many 3-digit, 4-digit, or 5-digit numbers can be made using the digits of 46723819?
6. How many numbers between 999 and 9999 are divisible by 5 and have no repeated digits?
7. How many ways can you order the letters in KEYBOARD if K and Y must always be kept together?
8. How many ways can 4 rock, 5 pop, and 6 classical albums be ordered if all albums of the same genre must be kept together?
9. In how many ways can the letters from the word EDITOR be arranged if vowels and consonants alternate positions?
10. If 8 boys and 2 girls must stand in line for a picture, how many line-up’s will have the
How many two-digits numbers can be made from the digits 6,7 and 8 if repetition of the digits is allowed
