A doctor is seeking an anti-depressant for a newly diagnosed patient. Suppose that, of the available anti-depressant drugs, the probability that any particular drug will be effective for a particular patient is p = 0.36. What is the probability that the patient will need to a. take 4 different drugs until the effective one is found. b. take 5 different drugs until the effective one is found. c. take 7 different drugs until the effective one is found.
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.
A doctor is seeking an anti-depressant for a newly diagnosed patient. Suppose that, of the available anti-depressant drugs, the probability that any particular drug will be effective for a particular patient is p = 0.36. What is the probability that the patient will need to
a. take 4 different drugs until the effective one is found.
b. take 5 different drugs until the effective one is found.
c. take 7 different drugs until the effective one is found.
a. P[drug ineffective]= 1-P[drug effective]=1-0.36=0.64
Event that the patient will need to take 4 different drugs until the effective one is found is same as the
event that the patient will have initial three drugs ineffective but fourth drug should be a effective one,
hence,
P[patient will need 4 different drugs until effective one is found]=
P[initially three drugs ineffective but fourth drug should be a effective one ]
= P[first drug ineffective]P[second drug ineffective]P[third drug ineffective]P[ fourth drug effective]
= (0.64)30.36= 0.094
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