A recent study to determine the efficacy of a diagnostic tool consisted of a sam
ID: 3352987 • Letter: A
Question
A recent study to determine the efficacy of a diagnostic tool consisted of a sample of 400 patients. Three hundred were known to be positive. A total of 280 tested positive. Of the patients that tested positive, 250 were known positive.
Let T be the event that a patient tests positive
Let K be the event that a patient is known to be positive
a) Show the joint probability table
b) Are T and K independent events? Explain.
c) What is the probability that a patient that tests negative is actually negative? What is the probability that a patient tests negative, when we know she/he is actually negative? Explain the difference.
Explanation / Answer
Ans:
a)
b)For T and K to be independent,
P(T and K)=P(T)*P(K)
Check:
P(T and K)=0.625
P(T)=0.75*0.7=0.525
Both are not equal,so T and K are not independent.
c)P(K'/T')=P(T' and K')/P(T')=0.175/0.3=0.583
P(T'/K')=P(T' and K')/P(K')=0.175/0.25=0.7
T T' Total K 250 50 300 K' 30 70 100 Total 280 120 400 Joint probability table T T' Total K 0.625 0.125 0.75 K' 0.075 0.175 0.25 Total 0.7 0.3 1