The probability of decreasing their separation (b) The probability of increasing their separation (c) The probability of no separation between them
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.
Two drunk start out together at the origin, each having the equal probability of
making a step to the left or right along the x-axis. Assume that men make their
steps simultaneously. Let N be the total number of steps taken by each man. Assume
that a particular instant, they are separated by some distance. In this situation, in
a given particular step.
If they move towards each other, the separation between them decreases.
If the move away from each other, the separation between them increases
If they move in the same direction, the separation remains unaltered
Then calculate
(a) The probability of decreasing their separation
(b) The probability of increasing their separation
(c) The probability of no separation between them
Out of N steps, n1 steps belong to decreasing the separation of them; n2 steps belong
to increasing the separation of them and n3 steps belong to no separation. Then,
calculate the following.
(d) The probability of taking the steps n1, n2 and n3
(e) The probability that they meet again at N steps
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