Math p
Shiindia
Prob1-3.docxName: weeks 1-3
Probability Island
You will create a population for an island community and collect the data by using and evaluating probability models. From these models, you will predict population growth and create graphs.
Your ship is carrying 150 passengers – 75 adult females and 75 adult males – all in good health. An intense storm occurs and your ship hits rocks and wrecks off the coast of a deserted island in the Pacific Ocean. This island has the necessary natural resources for human survival.
The ages of your passengers are recorded in the table below.
|
Age |
Female |
Male |
|
20-29 |
10 |
10 |
|
30-39 |
10 |
10 |
|
40-49 |
10 |
10 |
|
50-59 |
15 |
15 |
|
60-69 |
15 |
15 |
|
70+ |
15 |
15 |
|
Total |
75 |
75 |
Directions: Probability of births
For each women aged 20-39, roll a die one time. If you get a 6, the woman has a baby. Flip a coin. If it’s heads, it’s a girl. If it’s tails, it’s a boy. Complete the chart on the next page to track the births per year and the number of boys and girls. Repeat this simulation for ten years. Note: There are 20 women in these age groups. They are numbered 1 through 20 in the chart.
Questions:
1. Compare the theoretical probability to the experimental probability. Discuss the similarities and differences.
Probability measures the chances of occurrence for certain event bound to be undertaken. Probability can either be experimental or theoretical as this summary shall determine. Theoretical probability is founded on the basis of reasoning in that an opinion is formed around a certain event occurring. Theoretical probability can be generalized as a logical assumption of outcomes of certain events. For example, in an event where a fair dice with 6 sides is rolled, a logical outcome expectation is that there is an equal probability of occurrence for all the sides. This means that the probability of rolling the dice and getting sides 1, 2 3, 4, 5, and 6 is equal. The basis upon theoretical probability is formed differs from the experimental probability in that it is based on actual results from an experiment. Experimental probability is based on performing of the actual experiments and recording the outcomes.
In experimental probability there is no assumptions made on the outcomes of an event prior to performing the experiment. The judgement upon which probability of occurrence of events is based in experimental probability is derived from the results obtained. For example, a fair dice with 6 sides rolled would generate different results from the assumed probability assertions of equal chances of outcomes occurrence. Sample results for such a probability when the dice is rolled 10 times would show the following outcomes; the side labelled 1 appear 2 times, side labelled 4 three times, side labelled 3 one time, side labelled 5 two sides and side labelled 3 times. This results outcome is the complete opposite of the assumption made by theoretical probability. The similar part for both probability approaches is that if enough experiments are performed the results from experimental probability near the logical assumptions made in theoretical probability.
|
Woman |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |
Year 7 |
Year 8 |
Year 9 |
Year 10 |
|
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
|
2 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
|
3 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
4 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
|
5 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
|
6 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
|
7 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
8 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
|
9 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
|
10 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
|
11 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
|
12 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
|
13 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
|
14 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
15 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
|
16 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
|
17 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
18 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
|
19 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
|
20 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
|
total |
6 |
6 |
7 |
8 |
8 |
6 |
9 |
7 |
7 |
9 |
2. Assuming the births occur as recorded above, and that no one dies, what is the population of your island at the end of the ten-year period? Provide a chart that clearly shows the population of your island at the end of each year.
The population total for the island after ten years based on the probabilities above would be:
6 + 6 + 7 + 8 + 8 + 6 + 9 + 7 + 7 + 9 = 73 children.
The total population is; 150 + 73 = 223 people.
The following is bar chart showing the population of the island over the years.
Andrew, L. (2009). Experimental probability in elementary school. Teaching Statistics, 31(2), 34-36.
Prodromou, T. (2012). Connecting experimental probability and theoretical probability. ZDM, 44(7), 855-868.
