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Published byHillary Stone Modified over 9 years ago
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Simulating Experiments By: Justin Ross Tim Dietrich Brandon Izumi
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What is a Simulation? A simulation is an imitation of chance behavior, based on a model that accurately reflects the experiment under consideration.
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Why use Simulations? It is much easier to simply use a model to simulate a number of repetitions of the experiment than to repeat the actual experiment. You will save much time with simulation; and with the aid of a TI- 83/89 or a computer, the problems become much easier and quicker to solve.
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Simulation Steps 1.State the problem or describe the experiment. 2.State the assumptions. 3.Assign digits to represent outcomes. 4.Simulate many repetitions. 5.State your conclusions.
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Step One State the problem or describe the experiment. –What is the likelihood that in a family of four, there will be two girls and two boys?
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Step Two State the assumptions. –There is equal chance for having a boy or a girl. –Children are independent of each other; meaning that the gender of one child will not influence the gender of the next child.
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Step Three Assign digits to represent outcomes. –Table B will be used from the back of the book, starting with line 101. –Each digit in the table will represent a child being born. –Odd digits will represent girls; even digits will represent boys.
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Step Four Simulate many repetitions. –For this I will use 30 families of four. Digits – 1922 3950 3405 7562 8713 Sex ffmm fffm fmmf ffmm mfff 2&2 Yes No Yes Yes No 25 additional repetitions were done making 30 total repetitions; 11 families had two boys and two girls.
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Step Five State your conclusions. –I estimate that the probability of a family of four having two boys and two girls being 11/30 or 37%. This may be inaccurate, do to the fact that our simulation only had 30 repetitions. A calculator can easily be programmed to do thousands of repetitions.
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