Effective Paraphrasing Strategies
CHAPTER 5: PROBABILITY
5.1 RANDOMNESS, PROBABILITY, AND SIMULATION
LAW OF LARGE NUMBERS
Law of Large Numbers:
the proportion of times that a particular outcome occurs
in many repetitions will approach a single number.
Sometimes it is erratic, but
stabilizes eventually.
http://digitalfirst.bfwpub.com/stats_applet/stats_applet_10_prob.html
Probability
: The probability of any outcome of a chance process is
a number
between 0 and 1
that describes the proportion of times the outcome would occur in
a very long series of repetitions.
Make sure your answer makes sense!!!
On the calculator: 2.3844823E-8
Don’t tell me the answer is 2.38.
SIMULATIONS
A model
that accurately reflects the situation
1.
Ask a question of interest about some chance process
(Usually done for you)
2.
Describe how to use a chance device to imitate one repetition of the process. Tell
what you will record at the end of each repetition.
(Describe your plan)
3.
Perform many repetitions of the simulation.
(At least 25 on your homework)
4.
Use the results of your simulation to answer the question of interest.
(Conclusion)
EX 1:
At their annual picnic, 18 students in the math department at a university decide to play a softball game.
Twelve of the 18 students are math majors and 6 are stats majors. To divide into two teams of 9, one of
the professors put all of their names into a hat and drew out 9 players to form one team, with the
remaining 9 players on the other team. The players were surprised when one team was made up of
entirely math majors. Is it possible the names weren’t mixed well in the hat or could this happen by
chance? Design and carry out a simulation to help answer this question.
Plan:
Question
Number the math majors 1-12
and the stats majors 13-18. Use
technology to pick 9 unique
numbers between 1-18 for one
team. Record whether the team
was all math majors (#1-12).
Simulation:
__ out of __ trials had an
entire team of math majors.
Conclusion:
*Anything less than 5% is considered unlikely
*Make sure you
answered the question
Learn the art of paraphrasing by putting author's ideas into your own words to enhance understanding and clarity. Master paraphrasing techniques through examples and helpful tips, like simplifying complex sentences and utilizing synonyms.
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Presentation Transcript
CHAPTER 5: PROBABILITY 5.1 RANDOMNESS, PROBABILITY, AND SIMULATION
LAW OF LARGE NUMBERS Law of Large Numbers: the proportion of times that a particular outcome occurs in many repetitions will approach a single number. Sometimes it is erratic, but stabilizes eventually. http://digitalfirst.bfwpub.com/stats_applet/stats_applet_10_prob.html Probability: The probability of any outcome of a chance process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions. Make sure your answer makes sense!!! On the calculator: 2.3844823E-8 Don t tell me the answer is 2.38.
SIMULATIONS A model that accurately reflects the situation 1. Ask a question of interest about some chance process (Usually done for you) 2. Describe how to use a chance device to imitate one repetition of the process. Tell what you will record at the end of each repetition. (Describe your plan) 3. Perform many repetitions of the simulation. (At least 25 on your homework) 4. Use the results of your simulation to answer the question of interest. (Conclusion)
EX 1: At their annual picnic, 18 students in the math department at a university decide to play a softball game. Twelve of the 18 students are math majors and 6 are stats majors. To divide into two teams of 9, one of the professors put all of their names into a hat and drew out 9 players to form one team, with the remaining 9 players on the other team. The players were surprised when one team was made up of entirely math majors. Is it possible the names weren t mixed well in the hat or could this happen by chance? Design and carry out a simulation to help answer this question. *Make sure you answered the question Question Plan: Number the math majors 1-12 and the stats majors 13-18. Use technology to pick 9 unique numbers between 1-18 for one team. Record whether the team was all math majors (#1-12). Simulation: Conclusion: = ___, so the probability of getting an entire team of math majors is very unlikely* to happen by chance alone. There is convincing evidence the names weren t mixed well in the hat.* __ out of __ trials had an entire team of math majors. *Anything less than 5% is considered unlikely
