Question

A test to determine whether a certain antibody is present is 99.7% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject). The probability of a test coming back positive when the antibody is not present (a false positive) is 0.003. Suppose the test is given to seven randomly selected people who do not have the antibody.

Answer 1

to solve the given problem, you must multiply the probability that the antibody is not present which is 0.003 to the total number of people being tested.
number of no antibody = 7 * 0.003
number of no antibody = 0.021 which is already about 0

so there are no people that will not contain the antibody, because the probability to begin with is very small.

Answer 2

The probability that the test comes back negative for all seven people

is
`0.979`

Explanation:

Complete question

a) What is the probability that the test comes back negative for all seven people?

Solution -

Give -

The probability of false positive is
`0.003`

As we know that the knowing the result of testing for one individual gives us no information about what the result will be for the next person. Hence, one this is clear that this is an independent event.

Thus, the probabilities of getting a negative test for all seven individuals will be multiplied

Thus, the probability that the test comes back negative for all seven people

is

`= 0.997 * 0.997 *0.997 *0.997 *0.997 *0.997*0.997 \\= 0.997^7\\= 0.979`