A quick and inexpensive blood test is introduced to screen for a disease which w

Question

A quick and inexpensive blood test is introduced to screen for a disease which we will call D2. When people who have the antibodies for D2 in their blood have the screening test, they have a 90% chance of getting a + result (and a 10% chance of a negative result). When people who do not have the antibodies for D2 in their blood have the screening test, they have a 10% chance of getting a + result (and a 90% chance of a negative result). Assume that 10% of the population have the antibodies in their blood. A random person has a screening blood test. What is the probability that the test comes back negative? this probability cannot be determined from the information in the question 0.74 0.26 0.18 0.82

Explanation / Answer

Let D2 shows the event that person has antibodies and N shows the event that person do not have anti bodies in his blood. Let "+" shows the event that the test comes positive and "-" shows the event that test comes negative.

So we have follwoing probabilties:

P(D2)=0.10

P(N)=1-0.10=0.90

P(+|D2)=0.9

P(-|D2)=0.10

P(+|N)=0.1

P(-|N)=0.9

Here we have to find the probability P(-) so by conditional probability rules we have

P(-)=P(-|D2)P(D2)+P(-|N)P(N)=0.1*0.1+0.9*0.9=0.01+0.81=0.82

Hence, last option is correct.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---