Consider two medical tests, a and b for a virus. test a is 90% effective at recognizing the virus when it is present, but has a 5% false positive rate. test b is 80% effective at recognizing the virus when it is present, but only has a 1% false positive rate. the two tests are independent (i. e., they use different means for identifying the virus). the virus is carried by 2% of all people. if you could use only one of the two tests to identify the virus, which would you choose? justify your answer mathematically. how much more certain can you be if you can use both tests?

1

P(V|A) is not 0.95. It is opposite:

P(A|V)=0.95

From the text we can also conclude, that

P(A|∼V)=0.1

P(B|V)=0.9

P(B|∼V)=0.05

P(V)=0.01

P(∼V)=0.99

What you need to calculate and compare is P(V|A) and P(V|B)

P(V∩A)=P(A)⋅P(V|A)⇒P(V|A)=P(V∩A)P(A)

P(V∩A) means, that Joe has a virus and it is detected, so

P(V∩A)=P(V)⋅P(A|V)=0.01⋅0.95=0.0095

P(A) is sum of two options: "Joe has virus and it is detected" and "Joe has no virus, but it was mistakenly detected", therefore:

P(A)=P(V)⋅P(A|V)+P(∼V)⋅P(A|∼V)=0.01⋅0.95+0.99⋅0.1=0.1085

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).