Question

Simulation blunders Explain what’s wrong with each of the following simulation designs.

(a) A roulette wheel has $38$colored slots—$38$ red, $18$ black, and $2$green. To simulate one spin of the wheel, let numbers $00$ to $18$ represent red, $19$ to $37$

represent black, and $38$ to $40$ represent green.

(b) About $10\%$ of U.S. adults are left-handed. To simulate randomly selecting one adult at a time until you find a left-hander, use two digits. Let $01$ to $10$ represent being left-handed and $11$ to $00$ represent being right-handed. Move across a row in Table D, two digits at a time, skipping any numbers that have already appeared, until you find a number between $01$ and 10. Record the number of people selected.

Short answer

Part (a) The Simulation is incorrect.

Part (b) About $10\%$people are left-handed. In the Simulation, they're almost correct.

Step-by-step solution

Part (a) Step 1. Given Information 

The simulation designs are available for download. It is necessary to determine what is wrong with each of them.

Part (a) Step 2. Concept Used  

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$ (never happens) and $1$(happens frequently) (always occurs).

Part (a) Step 3. Explanation   

There are$18$red slots, $18$black slots, and two green slots on a roulette wheel. Red is represented by the numerals $00$to $18$, which are $19$numbers, i.e. $(00,01,02,03,04,05,06,07,08,09,10,11,12,13,14,15,16,17,18)$

Black is represented by the numerals $19$to $37$, which are numbers, i.e.

$(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)$

Green is represented by the numerals $38$through $40$, which are three numbers $(38,39,40)$We then notice that we have one number too many for each color, indicating that the stimulation, in this case, is incorrect.

Part (b) Step 1. Explanation  

Looking at this section, we can conclude that it is not suitable to skip over numbers that have already occurred because the likelihood of selecting a left-handed person will no longer be $10\%$If the first person chosen was $09$, for example, that person was left-handed. If we omit this number, the number $00$$08$corresponds to left-handed persons, whereas the numbers correspond to right-handed people, implying that we have $9$out of $9$odds of selecting a left-handed person, which is no longer $10\%$