The testing division of a chip manufacturing company tests all manufactured chips individually, one at a time. Based on the company data, with probability 0.9, the first defective chip tested on a given day appears after the 10th tested chip. Find the probability that the first defective chip appears between the 20th and the 30th tested chips excluding the 20th and the 30th chips on a given day.
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.
The testing division of a chip manufacturing company tests all manufactured chips individually, one at a time. Based on the company data, with
between the 20th and the 30th tested chips excluding the 20th and the 30th chips on a given day.
Introduction to Geometric distribution:
Suppose there are independent trials and the probability of success is same in each trial, then the probability of x trials for preceding the first success is qx-1p.
The outcome of each trial can be classified as either a “success” or a “failure”. The numerical value “1” is assigned to each success and “0” is assigned to each failure.
Moreover, the probability of getting a success in each trial, p, remains a constant for all the n trials. Denote the probability of failure as q. As success and failure are mutually exclusive, q = 1 – p.
Let the random variable X denote the number of trials. Thus, X can take any of the values 0,1,2,…,
Then, the probability distribution of X is a Geometric distribution with parameters (p) and the probability mass function (pmf) of X is given as:
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