marbles and 11 small marbles. Each marble is eith lected from the box, what is the probability that it is
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.
Let L denote the large marbles and S denote the small marbles.
Let G denote the green marbles and W denote the white marbles.
The number of large marbles is, n(L) = 19
The number of small marbles is, n(S)=11
The total number of marbles is,
n(L)+n(S)=19+11=30
The number of large marbles are green is,
n(L and G) =5
Thus, the number of large marbles are white is the difference between the number of large marbles and the number of large marbles are green.
That is,
n(L and W ) = n(L)- n( L and G) =19-5=14
The number of small marbles are white is,
n(S and W)=3
Thus, the number of small marbles are green is the difference between the number of small marbles and the number of small marbles are white
That is,
n( S and G)= n(S)-n( S And W)= 11-3=8
The total number of green marbles is,
n(G)= n( L and G) +n( S and G)= 5+8=13
The total number of white marbles is,
n(W) =n( L and W) +n( S and W)=14+3=17
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