Question

Intense or repetitive sun exposure can lead to skin cancer. Patterns of sun exposure, however, differ between men and women. A study of cutaneous malignant myeloma in the Italian population found that 15% of skin cancers are located on the head and neck, another 41% on the trunk, and the remaining 44% on the limbs. Moreover, 44% of the individuals with a skin cancer on the head are men, as are 63% of those with a skin cancer on the trunk and only 20% of those with a skin cancer on the limbs. What percent of all individuals with skin cancer are women?

Answer 1

P(head and neck) = 0.15

P(trunk) = 0.41

P(limbs) = 0.44

P(men | head and neck) = 0.44

P(men | trunk) = 0.63

P(men | limbs) = 0.2

P(men) = P(men | head and neck) * P(head and neck) + P(men | trunk) * P(trunk) + P(men | limbs) * P(limbs)

             = 0.44 * 0.15 + 0.63 * 0.41 + 0.2 * 0.44

             = 0.4123

P(women) = 1 - P(men) = 1 - 0.4123 = 0.5877 (ans)