finite please help with both thanks! A diagnostic test is a procedure which give
ID: 3222165 • Letter: F
Question
finite please help with both thanks!
A diagnostic test is a procedure which gives a quick, but not always reliable, indication of whether a patient has a certain disease. Test results are said to be "positive" if, after testing, the person Is thought to have the disease and 'negative" if the person is thought not to have the disease. In a particular region, 5% of the population is thought to have a certain disease. A standard diagnostic test has been found to correctly identify 94% of the people who have the disease. However, the test also incorrectly diagnoses 8% of those who do not have the disease as having the disease {in other words, the person does not have the disease but the test them that they do). A randomly selected person in the region is tested for the disease. What is the probability the test comes back positive? What is the probability the test comes back positive and the person actually has the disease? If the test comes back positive, what then is the conditional probability that the person actually does have the disease? In Major League Baseball. the American League Championship Series is a playoff round that determines the winner of the American League pennant. The winner of the series advances to play the winner or the National League Championship Series in baseballs championship, the wend Series, The American League Championship Series s a "best-of-seven series". This means that the winning team must win 4 games to win the series. Once a team wins 4 games the series ends and no additional games are played. Therefore, the series might be as short as 4 games (If one team wins the first four games) or it might be as IONG as 7 games. In the 2004 American League Championship Series the Boston Red Sox played the New York Yankees The Yankees won the first three games, but the Red Sox rolled and won the last four games to win the series. This was the first time in the history of Major League baseball that a team had come from a 3-0 deficit to wm a 7-game playoff series. Scenario: Suppose Teams A and B are playing a 'best-of-seven' series. Assume that the games form independent trials where in each game played the probability that Team A wins is 0.64 and the probability that Team B wins is 0.36. WhatExplanation / Answer
let probabilty of having disease =P(D)=0.05
a)and probabilty of test postive =P(P)=P(D)*P(P|D)+P(Dc)*P(P|Dc)=0.05*0.94+0.95*0.08=0.123
b)=P(P)*P(P|D)=0.05*0.94=0.047
c)P(D|P)==P(D)*P(P|D)/P(P)=0.05*0.94/0.123=0.3821
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