A Department of Health report states: \"If a tested patient has the disease, the

Question

A Department of Health report states: "If a tested patient has the disease, then the test will indicate 'positive 99% of the time; and if a tested patient does not have the disease, then the test will indicate "negative 95% of the time. Supposing that only one in a thousand of the population has that disease, calculate the probability that the tested patient has the disease given that the test was positive. Supposing that only one in a thousand of the population has that disease, calculate the probability that the tested patient has the disease given that the test was negative.

Explanation / Answer

Follwoing table is formed with the given inforamtion

Calculate the probability that the tested patient has the diease given that test was positive

Probability that the tested patient has the diease given that test was positive =

Number of patients tested positive and having diease / Number of patients tested positive

From the table,

Number of patients tested positive and having diease = 0.99

Number of patients tested positive = 50.94

Probability that the tested patient has the diease given that test was positive = 0.99/50.94 =0.019434

Calculate the probability that the tested patient has the diease given that test was negative

Probability that the tested patient has the diease given that test was negative=

Number of patients tested negative and having diease / Number of patients tested negative

From the table,

Number of patients tested negative and having diease = 0.01

Number of patients tested positive = 949.06

Probability that the tested patient has the diease given that test was negative= 0.01/949.06 = 0.000010537

Having Disease Not Having Disease Total Test Positive 1x99/100 =0.99 999-949.05=49.95 49.95+0.99=50.94 Test Negative 1-0.99 =0.01 999x95/100 = 949.05 949.06 Total 1 999 1000

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.