Question

A test to determine whether a certain antibody is present is 99.1​% effective. This means that the test will accurately come back negative if the antibody is not present​ (in the test​ subject) 99.1​% of the time. The probability of a test coming back positive when the antibody is not present​ (a false​ positive) is 0.009. Suppose the test is given to six randomly selected people who do not have the antibody. ​(a) What is the probability that the test comes back negative for all six ​people? ​(b) What is the probability that the test comes back positive for at least one of the six ​people?

Answer 1

Answer:

The probability that all the six people will test negative for the antibody is 0.9472.

The probability that the test comes back positive for at least one of the six ​people is 0.0528

Step-by-step explanation:

Consider the provided information.

probability that antibody is present will be effective is 99.1​% and not present​ is 99.1​% of the time.

Part (A)What is the probability that the test comes back negative for all six ​people? ​

Let P(X)= P(Antibody not present)

We want test comes back negative for all six that means antibody is present for all six. Thus X=0

$P(X=0)=0.991\times0.991\times0.991\times0.991\times0.991\times0.991\\P(X=0)=0.9472$

The probability that all the six people will test negative for the antibody is 0.9472.

Part (B) What is the probability that the test comes back positive for at least one of the six ​people?

$P(X \geq1)=1-P(X=0)$

$P(X \geq1) = 1-0.9472$

$P(X \geq1) = 0.0528$

Hence, the probability that the test comes back positive for at least one of the six ​people is 0.0528