Question
I have completed most of the problem; however, I am stuck on the last part of this problem. The first image is the overview of
I have completed most of the problem; however, I am stuck on the last part of this problem.
The first image is the overview of the problem.
The second image is the completed charts.
The third image is the calculation of the theoretical probability.
The fourth image is the calculation for the experimental probability.
The fifth image is the part where I am stuck- It says to compare the theoretical probability and experimental probability and to explain any differences or similarities. I am somewhat knowledgeable about the differences and similarities between theoretical probability and experimental probability; however, I am unsure of how to compare and contrast the theoretical probability and experimental probability to this specific problem.
Probability Island You will collect the data for the population of an island community. Then you will use project. and evaluate probability models. You will be using this data for the next parts of your 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. a. Calculate the theoretical probability and the experimental probability of the births. Show your work. b. Compare the theoretical probability to the experimental probability. C. Discuss any similarities and/or differences. You may consider the annual or gender rates or any other possibility.Chart 1. Woman Year Year Year Year Year Year 9 10 1- 2 3 4 12 13 14 15 16 17 18 19 20 Total boy's 1 14 3 4 2 3 Total girls 3 2 3 4 3 3 3 Total 3 15 15 16 Births Chart 2 Year 1 2 3 4 5 6 7 8 9 10 Male 75 80 25 40 Female 75 85 193 47 100 03 106 Total 150 153 64 167 173 1783 188 95 200 206Theoretical Probability Since we are determining if a woman gives birth by rolling a 6 on a fair dice, the theoretical probability of a women giving birth is 1/6. As for determining the gender of the child, the theoretical probability is % since, there are two possibilities (boy or girl). The probability for a woman giving birth to a boy or a girl in a year is the probability of rolling a 6 and the probability of the child being a girl or boy. Equation: P(Girl) = P (Boy)= 1/6 * %% =1/12 Year P (Boy is Born) | P (Girl is Born] P (Baby is P (Boy/Birth) P (Girl/Birth) Born) 0.083 0.083 0.167 0.5 0.5Experimental Probability The experimental probability is the probabilities of births (for a boy born, a girl born, and total births. Year P (a boy is P (a girl is born) P (a baby is P (boy/birth) = P (girl/birth) born) = B/20 = G/20 born) = T/20 B/T =G/T 1 0.05 0.1 0.15 0.33 0.67 2 0.2 0.35 0.55 0.36 0.64 3 0.1 0.05 0.15 0.67 0.33 0.15 0.15 0.3 0.5 0.5 5 0.1 0.1 0.2 0.5 0.5 6 0.15 0.15 0.3 0.5 0.5 0.05 0.2 0.25 0.2 1.8 0.2 0.15 0.35 0.57 0.43 0.1 0.15 0.25 0.4 0.6 10 0.15 0.15 0.3 0.5 0.5What part I need help with: b. Compare the theoretical probability to the experimental probability. c. Discuss any similarities and/or differences. You may consider the annual or gender rates or any other possibilityStep by Step Solution
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