Question

Question 5. (20 pts.) 1. The probability that a person selected at random from a population will exhibit the classic symptom of a certain disease is 0.2, and the probability that a person selected at random has the disease is 0.23. The probability that a person who has the symptom also has the disease is .18. A person selected at random from the population does not have the symptom. What is the probability that the person has the disease? 2. In a certain population of women 4 percent have had breast cancer, 20 percent are smokers, and 3 percent are smokers and have had breast cancer. A woman is selected at random from the population. What is the probability that she has had breast cancer or smokes or both?

Answer 1

1) P(has the disease | doesn't have the symptom)

= P(has the disease and doesn't have the symptom)/P(doesn't have the symptom)

= (P(has the disease) - P(has the disease and have the symptom))/P(doesn't have the symptom)

= (0.23 - 0.18)/(1 - 0.2)

= 0.05/0.8

= 0.0625

2) P(breast cancer or smokes or both) = P(breast cancer) + P(smokes) - P(breast cancer and smokes)

= 0.04 + 0.2 - 0.03

= 0.21