Question

A certain disease occurs most frequently among older women. Of all age groups, women in their 60s have the highest rate of breast cancer. The National Cancer Institute (NCI) compiles U.S. epidemiology data for a number of different cancers. The NCI estimates that 3.12% of women in their 60s get breast cancer. Mammograms are X-ray images of the breast used to detect breast cancer. A mammogram can typically identify correctly 81% of cancer cases and 92% of cases without cancer. If a woman in her 60s gets a positive mammogram, what is the probability that she indeed has breast cancer? Select one: O a. 0.246 O b. 0.897 c. 0.392 d. 0.891 o e. 0.103

Answer 1

Answer is A .2468

Hele By Bayes theorem we can solve this Que probability to have cancer. ple/postve) - [PC] & pl Positivel] [PE]* Ploositue () + Abegninger i bagning e P@)-Irobability of women having cances. - P(positivek) = Probability of result having positive -) e (begnign) =) No cancer - P (Positive Rognian) =) Postive no harmful. No cancee give Ple] = 3.12 % =) 0.0312 P(begnan) = -0.0312 20.9668 P (Positiveld - si% Depostil besn)- 92% p(Negative) 1.92=0.80 2.92 - RO) - .0312x. 81 (6312*+81 +.96888.05) = Rs 0.246