Homework Answers

Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 19 of the 49 boxes on the shelf have the secret decoder ring. The other 30 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?

Question 1.13 [2, 2, 3]

Due to COVID-19 there was no time to have the swimming gala at your old primary school. The

principal knows that you are currently studying statistics and he wants you to help with this

probability problem. The principal tells you that out of the 8 swimmers, 3 are from grade 4, 2 are

from grade 5 and 3 are from grade 6. Since no Gala can be held the principal selects swimmers at

random to attend the EP school Gala, the first student selected at random will be representing the

schools fastest swimmer, while the second student selected will represent the school second fastest

swimmer.

Help the principal to answer the following questions:

a) What is the probability that the two fastest swimmers are from Grade 6?

b) What is the probability that fastest swimmer is from Grade 4 and the second fastest from

Grade 6?

c) Timothy is a student in grade 5, what is the probability that he will either come first or second?

Question 1.12 [2, 3]

Catherine has a Gmail account and categorises her emails according to work and non-work related

emails. The probability that an email is a work-related email is 65.32%. Suppose furthermore it is

given that the probability that a work-related email received is a spam email is 15.34% and that if it

is a non-work related email that it is spam is 5.6%.

Calculate the following probabilities

a) That an email received by Catherine is a spam email.

b) Given that the email is spam what is the probability that it is a non-work-related email.

Question 1.11[4]

There are two bags of chocolates. Bag one has 5 Barones and 2 KitKats and Bag 2 has 2 Barones

and the 7 KitKats. A chocolate is selected at random from Bag one and added to Bag two. A

chocolate is now drawn randomly from Bag two. Given that the chocolate selected is a KitKat what

is the probability that the original chocolate drawn from Bag one was a Barone? Show all working

out.

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?