Question One
Question
A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. For example, the probability of rolling a six is three times as probable as rolling a two.
- Write down a sample space for the experiment of rolling this die.
- Work out the probability function for this die.
- What is the probability of getting an even number in one throw?
Solution
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Question Two
Question
Two dice are thrown. What is the probability that…
- …exactly one of them is a six.
- …at least one of them is a six.
- …at least one of them is greater than three.
You may want to draw a 6 by 6 table labelling the states to help you.
Solution
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Question Three
Question
A coin is tossed twelve times. Find the probability that a coin turns up heads for the first time on the tenth, eleventh, or twelfth toss.
Solution
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Question Four
Question
In a certain residential suburb, 60% of all households get Internet service from the local cable company, 80% get television service from that company, and 50% get both services from that company. If a household is randomly selected, what is the probability that it gets at least one of these two services from the company, and what is the probability that it gets exactly one of these services from the company?
Solution
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Question Five
Question
An entrepreneur has 5 possible locations to base his business. If she awards each site a mark out of five (1,2,3,4,5) how many distinct scorecards are possible - if there are no restrictions in the assessment - the sites must be ranked in order of preference (no repetitions, in other words) - she is only interested in the top 2 ranked sites.
Solution
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Question Six
Question
Give an answer the following questions:
- How many different ways can a chairperson and assistant chairperson be selected for a research project, if there are 7 students available?
- How many teams of two joint chairpeople, with equal powers, be selected for a research project, if there are 7 students available?
- How many distinct words can be formed using all the letters of the word ’supercalifragilisticexpialidocious’. Distinct words are orderings of letters that you could tell apart without having to label letters (and they don’t have to be in the dictionary).
Solution
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Question Seven
Question
A coin is tossed twice. Consider the following events:
- Heads on the first toss.
- Heads on the second toss.
- The two tosses come out the same.
- Show that A, B, C are pairwise independent but not independent.
- Show that C is independent of A and B but not of A ∩B
Solution
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