STAT-3110-01 (Fall 2017)-Probability and Statistics n Alahmadi Test: Test 01 (ST
ID: 3306046 • Letter: S
Question
STAT-3110-01 (Fall 2017)-Probability and Statistics n Alahmadi Test: Test 01 (STAT-3110) om Time Remaining: 01:0102 Submit Test This Question: 1 pt om 17 of 22(11 complete) This Test: 75 pts possible pm The probability that a person has a certain disease is 0.05. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.88. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.02. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present? pm 117 | The probability is pm Round to three decimal places as needed) pm pm omExplanation / Answer
Let A denote the event of a person having a disease and B denote the event that the test will give a positive result.
Given P(A) = 0.05 P(B|A) = 0.88 P(B|Ac) = 0.02
P(A B) = P(A) P(B|A)
= 0.05 * 0.88
= 0.044
P(Ac) = 1 - 0.88 = 0.12
P(Ac B) = P(Ac) P(B|Ac)
= 0.12 * 0.02
= 0.0024
=> P(B) = P(A B) + P(Ac B)
= 0.044 + 0.0024 = 0.0464
P(A|B) = P(A B) / P(B)
= 0.044 / 0.0464
= 0.9483
The probability is 0.948.
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