It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance. Athletes are tested to see if they are using illegal drugs or not using illegal drugs and the test can come back positive or negative. The test for this drug is 90% accurate for non-drug users (this means there is a 90% chance the test comes back negative if the person is a non-user). What is the probability that an athlete tests negative and is not a user of an illegal drug

0.873 = 87.3% probability that an athlete tests negative and is not a user of an illegal drug

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Not a user of an illegal drug.

Event B: Tests negative.

The test for this drug is 90% accurate for non-drug users (this means there is a 90% chance the test comes back negative if the person is a non-user)

This means that

It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance.

So 100 - 3 = 97% probability that the athlete does not use the drug, so

What is the probability that an athlete tests negative and is not a user of an illegal drug

0.873 = 87.3% probability that an athlete tests negative and is not a user of an illegal drug

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.