first- and second-born children of two-children families by gender is shown below. What is the probability that a family with two children selected at random in this city has children of the same gender? First-born Female Male Total Female 540 512 1052 Male 492 456 948 Total 1032 968 2000
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.
In a certain city, the distribution of the first- and second-born children of two-children families by gender is shown below. What is the probability that a family with two children selected at random in this city has children of the same gender?
| First-born | Female | Male | Total |
| Female | 540 | 512 | 1052 |
| Male | 492 | 456 | 948 |
| Total | 1032 | 968 | 2000 |
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A family in this city with two children has a male first- born. What is the probability that its second- born is female?
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