Like all medical tests, a mammogram, a test for breast cancer, does not always detect accurately. It is estimated that mammograms produce 5% false positives (indicate cancer when there is none) and 10% false negatives (indicate no cancer when there is cancer). According to the CDC, the breast cancer rate among American women in 2020 was 0.0012.
a.) Create a tree diagram showing the probabilities of the results of mammograms.
Find these probabilities.
b.) P(tests positive | does not have breast cancer)
c.) P(tests negative | does not have breast cancer)
d.) P(has breast cancer and tests negative)
e.) P(does not have breast cancer and tests negative)
f.) P(tests accurately)
g.) P(tests inaccurately)