In a group of girls there are 10 girls with blue eyes, 12 girls with brown eyes and 6 girls with green eyes. In a group of boys there are 11 boys with blue eyes, 9 boys with brown eyes and 7 boys with green eyes. What is the probability of getting both a boy and a girl with blue eyes?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Given:
The number of girls with blue eyes are 10.
The number of girls with brown eyes are 12.
The number of girls with green eyes are 6.
The total number of girls are N=10+12+6=28.
The number of boys with blue eyes are 11.
The number of boys with brown eyes are 9.
The number of boys with green eyes are 7.
The total number of boys are M=11+9+7=27.
Define events:
Let G be the event representing the girls.
Let B be the event representing the boys.
Let E be the event representing the blue eyes.
So,
11.
10.
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