The results of many games of tennis between two players suggest that
player A has a 0.6 chance of winning a set against player B. The first
player to win two sets wins the match.
Design a simulation experiment to simulate the situation of a match
between A and B and hence estimate the probability that A wins the match.
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The BPQ Oil Company gives away a ‘lucky card’ with every purchase worth
$20 or more. There are five different ‘lucky cards’ in the set and when a
customer has collected each of the five different cards the customer
becomes eligible for a cash prize draw.
Design a simulation experiment to simulate t simulate this situation and estimate the
probability that a customer becomes eligible for the cash prize draw after
Six purchases
(of $20 or more)
Ten purchases
(of $20 or more)
Twenty purchases (of $20 or more)
What is the average number of purchases that a customer must make to collect a full
set.
A customer making a purchase worth $40 or more receives two lucky cards which are
guaranteed to be different. What is the probability that a customer making five
purchases (each worth at lest $40) becomes eligible for the cash prize draw.
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On average four out of every six kiwifruit selected at the orchard, are
suitable for export. Use a simulation technique (with random numbers
or dice) to estimate the probability that all of the next five kiwifruit
which are tested will be up to the export standard.
The LOTTO game uses 40 balls (numbered 1 to 40). Each week seven of the numbers
are randomly selected.
What is the probability that the number 1 will be the first number selected next
week.
What is the probability that the number 1 will be selected (as any one of the seven
numbers) next week.
What is the probability that the number 1 will be selected (as any one of the seven
numbers) at least once during the next ten weeks. Use a simulation method to
estimate this answer.
Describe in words how you would try to simulate each of the following using
numbers, dice etc.
You are required to find out about groups of five people and the numbers of lefthanded people in these groups. Assume that 10% of the population is left-handed.
You are required to find out about groups of five people and the number of smokers
in these groups. It is assumed that 25% of the population smoke.
You are required to find out about groups of five people and the number of smokers
in these groups, given that 23% of the populations is assumed to smoke.