A question of Conditional Probability?

Question

In a certain region of the country it is known from past experience that the probability of selecting an adult over 40 years of age with cancer is 0.05. If the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of incorretly diagnosing a person without cancer as having the disease if 0.06. what is the probability that a person is diagnosed as having cancer?

Answer 1

All 3 above answers are wrong.

probability of selecting person with cancer and correctly identifying it is: 0.05 * 0.78 = 0.039

probability of selecting person without cancer and incorrectly diagnosing them with cancer is: 0.95 * 0.06 = 0.057

Total probability of diagnosing someone with cancer is 0.039 + 0.057 = 0.096 or 9.6%.

And that is assuming we are only talking about the sample of adults over 40 years.

Answer 2

i think my argument should not be nicely received. I say the danger is 50% enable a ??, enable b ?? and randomly pick the values for a and b. As already pronounced, for a ? 0, P( a < b²) = a million, it really is trivial. in worry-free words truly a lot less trivial is the theory that P(a < 0 ) = a million/2 and accordingly P( a < b² | a ? 0) = a million and P( a < b² ) ? a million/2 Now evaluate what occurs even as a > 0 For a > 0, even as it really is elementary to prepare there's a non 0 probability for a finite b, the decrease, the danger is 0. a < b² is a similar as affirming 0 < a < b², undergo in recommendations we are in worry-free words observing a > 0. If this a finite period on a limiteless line. The probability that a is an ingredient of this period is 0. P( a < b² | a > 0) = 0 As such we've a complete probability P( a < b² ) = P( a < b² | a ? 0) * P(a ? 0) + P( a < b² | a > 0) * P(a > 0) = a million * a million/2 + 0 * a million/2 = a million/2 undergo in recommendations, that's because of the limitless contraptions. no remember what variety of period you draw on paper or on a pc you'll come across a finite probability that seems to frame of mind a million. yet that's because of the finite random variety turbines on the computer and if we had this question requested with finite values there will be a a answer more beneficial than 50%. i do not advise to be condescending, yet please clarify why making use of the Gaussian to approximate a uniform distribution is a strong theory? are not limitless numbers exciting. Cantor even as mad operating with them! :)

Answer 3

Start with 2000 adults. 100 of them have cancer. The diagnosis rate for them is 100 x 0.78 = 78, and for the others it is 1900 x 0.06 = 114. The total diagnoses for 2000 persons are 192, so the probability is 0.096.

This assumes that the doctor is as likely to see one of the 100 as to see one of the 1900, but if that's not true the answer is indeterminate.

Answer 4

the probability that a person is diagnosed as having cancer is 0.036

Answer 5

Okay, I think its (.05*.78) + (.95*.06) = .096.

Answer 6

0.039

Answer 7

0.79