Suppose 2 doctors A and B test all patients coming into a clinic for Syphilis. Let A+ = {doctor A makes a positive diagnosis} and B+ = {doctor B makes a positive diagnosis}. Suppose doctor A diagnoses 10% of all patients as positive, doctor B diagnoses 17% of all patients as positive and both doctors diagnose 8% of all patients as positive. i) Find the conditional probability that doctor B makes a positive diagnosis given that doctor A makes a positive diagnosis. ii) What is the conditional probability that doctor B makes a positive diagnosis of Syphilis given doctor A makes a negative diagnosis. iii) Suppose that a balanced die is tossed once. Find the probability of a 1, given that an odd number was obtained.
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.
Suppose 2 doctors A and B test all patients coming into a clinic for Syphilis. Let A+ =
{doctor A makes a positive diagnosis} and B+ = {doctor B makes a positive
diagnosis}. Suppose doctor A diagnoses 10% of all patients as positive, doctor B
diagnoses 17% of all patients as positive and both doctors diagnose 8% of all patients
as positive.
i) Find the conditional
that doctor A makes a positive diagnosis.
ii) What is the conditional probability that doctor B makes a positive diagnosis of
Syphilis given doctor A makes a negative diagnosis.
iii) Suppose that a balanced die is tossed once. Find the probability of a 1, given that
an odd number was obtained.
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