Will you please provide more information and state a clear question
is a right triangle with base length 1 and height 8, so the area of
is
.
The average value of
over
is given by the ratio
The denominator is just the area of
, which we already know. The average value is then simplified to
In the
-plane, we can describe the region
as all points
that lie between the lines
and
(the lines which coincide with the triangle's base and hypotenuse, respectively), taking
. So, the integral is given by, and evaluates to,
Nathan has an infection and he needs to be treated with penicillin
But there’s a 75% probability of him being allergic to penicillin
And to test if the skin reacts to penicillin, the test is 98% accuracy
So even if he has the allergy the test is only 98% accurate of identifying the allergy
Therefore we are asked to find the probability of both these events happening
Event 1 and event 2 both should happen then. When the ‘and’ function is used in probabilities then the probabilities of both events happening should be multiplied
Therefore probability that Nathan has the allergy and test predicts it is
= 75% x 98% = 0.735
The answer is D. 0.735
