Investigate the distribution of males&acute; and/ or females in families. You may choose, for example, to collect data on the distribution of girls in families of three children and to estimate the probability of a female birth.
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Introduction

Middle
The Binomial Model
The binomial model must be set so that the probability of having a boy is 0.5 and the probability of having a girl is set at 0.5. The number of times that the event must happen is 3.
The binomial model below is an example of how the final model will look it is possible from this to see how the mathematics are carried and set out.
N how many times the event happens
R Outcomes from the events
P The probability of the outcome
Using the results that will be obtained from the binomial model it will be possible to calculate the amount of families out of the 30 collected that should have 3 boys, 3 girls, 1 boy 2 girls or 2 boys 3 girls.
The 4 binomial models are below:
1 (no boys)
2 (one boy)
3 (two boys)
4 (three boys)
Results to Questionnaires
Number selected Amount of children in family Amount of boys Amount of girls
1 3 2 1
2 3 2 1
3 3 1 2
4 3 1 2
5 3 1 2
6 3 2 1
7 3 1 2
8 3 2 1
9 3 2 1
10 3 2 1
11 3 1 2
12 3 1 2
13 3 2 1
14 3 2 1
15 3 3 0
16 3 1 2
17 3 0 3
18 3 2 1
19 3 1 2
20 3 3 0
21 3 3 0
22 3 1 2
23 3 2 1
24 3 2 1
25 3 1 2
26 3 0 3
27 3 1 2
28 3 3 0
29 3 2 1
30 3 0 3
Conclusion
Looking at both sets of results it is possible to calculate the probability of having one or more boys in a family of three children. To work out the probability of having on or more boys in a family the probabilities of having one, two or three boys in a family must be added together. Below is the working for the real life and binomial probabilities.
Real world 0.366 + 0.4 + 0.133 = 0.899
Binomial 0.375 + 0.375 + 0.125 = 0.875
Therefore it is possible to conclude that the real world model and the binomial show a strong correlation and therefore proving the original hypothesis. They prove that there is not only a higher than 75% chance of having a boy in three but that there is actually a chance of almost 90%
This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.
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