2. Simulating Experiments By: Justin Ross Tim Dietrich Brandon Izumi

3. What is a Simulation? A simulation is an imitation of chance behavior, based on a model that accurately reflects the experiment under consideration.

4. 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.

5. 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.

6. 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?

7. 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.

8. 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.

9. 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.

10. 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.