Intro to Survey Mathematics

Name: weeks 1-3

Probability Island

You will collect the data for the population of an island community. Then you will use and evaluate probability models. You will be using this data for the next parts of your project.

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

1. For each woman 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 Chart 1 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. For the purposes of this project, assume all women in these age groups remain capable of having children; keep everyone in their assigned age groups.

2. Assuming the births occur as recorded, and that no one dies, what is the population of your island at the end of the ten-year period? Use Chart 2 to clearly show the population of your island at the end of each year.

3. Showing your work, calculate the theoretical probability and the experimental probability of:

a) A woman giving birth in any given year

b) Having a baby and it being a girl

c) Having a baby and it being a boy

4. Compare the theoretical probabilities to the experimental probabilities. Use these results to discuss any similarities and/or differences.

Chart 1.

Woman	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10
1	X	X	X	X	X	X	X	X	G	X
2	X	G	X	B	X	X	G	X	G	X
3	X	X	X	X	X	B	X	X	X	X
4	X	X	X	X	X	X	X	B	X	X
5	G	X	X	X	G	X	X	X	X	X
6	X	X	X	X	G	X	X	B	X	X
7	X	X	G	X	X	X	X	X	B	X
8	X	X	X	X	G	X	X	X	X	X
9	X	X	B	G	X	B	X	X	X	X
10	X	X	X	X	X	X	X	X	X	X
11	X	X	B	X	X	B	X	X	X	X
12	X	X	B	B	X	X	X	X	X	X
13	G	X	X	X	X	X	X	X	X	X
14	G	X	X	X	B	X	X	X	X	X
15	X	G	X	X	X	X	X	X	X	X
16	X	X	X	G	X	X	X	X	B	X
17	G	X	X	X	X	B	X	B	X	X
18	B	X	X	X	X	X	X	X	X	X
19	X	X	X	X	G	X	X	X	X	X
20	X	X	X	X	X	X	X	X	X	X
Total boys	1	O	3	2	1	4	0	3	2	0
Total girls	4	2	1	2	4	0	1	0	2	0
Total Births	5	2	4	4	5	4	0	3	4	0

Chart 2

Year	0	1	2	3	4	5	6	7	8	9	10
Male	75	76	76	79	81	82	86	86	89	91	91
Female	75	79	81	82	84	88	88	89	89	91	91
Total	150	155	157	161	165	170	174	175	178	182	182

3a- The probability of a woman having a baby any given year would be.

The probability would be ½. You have a total of 10 years and 20 women. So in 10 years its possible 20 women can give birth any given year.

3b- The probability of a woman having a baby and it being a girl would.

A total of 16 girls were born over the 10 years out of 20 women. That would be a total out of 4/5.

3c-The probability of a woman having a baby and it being a boy would be.

A total of 16 boys were born over the 10 years out of 20 women. That would also be a total of 4/5.

4. Out of 20 women in 10 years it is possible for any of them to get pregnant. 16 girls are born and 16 boys are born which is pretty even and would be the same just different genders.