An article in Journal of National Cancer Institute [“Breast Cancer Screening Policies in Developing Countries: A Cost-Effectiveness Analysis for India” (2008, Vol.100(18), pp. 1290–1300)] presented a screening analysis model of breast cancer based on data from India. In this analysis, the time that a breast cancer case stays in a preclinical state is modeled to be exponentially distributed with a mean depending on the state. For example, the time that a cancer case stays in the state of T1C (tumor size of 11–20 mm) is exponentially distributed with a mean of 1.48 years.

(a) What is the probability that a breast cancer case in India stays in the state of T1C for more than 2.0 years?

(b) What is the proportion of breast cancer cases in India that spend at least 1.0 year in the state of T1C?

(c) Assume that a person in India is diagnosed to be in the state of T1C. What is the probability that the patient is in the same state six months later?