For each test, there are only two possible outcomes. Either it is positive, or it is negative. The probability of a test being positive or negative is independent of any other test, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability of an individual blood sample testing positive for the virus is 0.06.

This means that $p = 0.06$

If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture.

It will be positive if at least one of the tests is positive, that is:

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

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.06)^{0}.(0.94)^{3} = 0.8306$

Then

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8306 = 0.1694$

0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.

8 0

2 years ago

Calculate the value of x .

Anika [276]

Answer:

25 degrees

Step-by-step explanation:

2x plus 310 degrees add up to a full circle: 360 degrees.

Therefore, 2x = 360 - 310, or 2x = 50, or x = 25 degrees

5 0

2 years ago

Hi answer for this please

miv72 [106K]

Answer:

x+79degree + 35degree = 180 degree ( being the sum of all angle of the triangle )

or, x + 114 degree = 180 degree

or, x = 180degree - 114degree

or, x = 66degree

hence, x = 66 degree.

3 0

2 years ago