The authors of a paper presented detailed case studies to medical students and to faculty at medical schools. Each participant was asked to provide a diagnosis in the case and also to indicate whether his or her confidence in the correctness of the diagnosis was high or low. Define the events C, I, and H as follows. C

C-event that diagnosis is correct
I - event that diagnosis is incorrect
H- event that confidence in the correctness of the diagnosis is high

(a) Data appearing in the paper were used to estimate the following probabilities for medical students.
P(C) = 0.262
P(HIC) = 0.344
P(I) = 0.738
P(H|I) = 0.074

Use Bayes' rule to compute the probability of a correct diagnosis given that the student's confidence level in the correctness of the diagnosis is high (Round your answer to three decimal places.)

0.623

Step-by-step explanation:

We have to find the probability that a diagnosis is correct given that confidence in the correctness of diagnosis is high i.e.P(C/H)=?

Using Bayes' theorem the probability can be computed as

We are given that

P(C) = 0.262 , P(H/C) = 0.344 , P(I) = 0.738  and P(H/I) = 0.074.

So,

P(C/H)=0.623 (rounded to three decimal places).

Thus, the probability that a diagnosis is correct given that confidence in the correctness of diagnosis is high is 0.623.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

168

step-by-step explanation:

i am pretty sure that the answer is 168