A quick and inexpensive blood test is introduced to screen f

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).

A person who has the antibodies in their blood has blood taken and sent to two independent laboratories to have the screening tests.

Determine (if possible) the probability at least one of the tests come back positive.

Solution

Answer is : 1 - P(D2 Negative)*P(D2 Negative)

= 1 - 0.1 * 0.1=0.99