4. About 85% of lung cancers are of non-small cell type, which includes adenocarcinoma, squamous cell carcinoma, large cell lung cancer, and other types of nonsmall cell lung cancer. Adenocarcinoma accounts for about 45%, squamous cell carcinoma accounts for about 30%, large cell carcinoma accounts for about 9%, and other types of non-small cell lung cancer account for about 1%.

(a) Given a patient who has non-small cell lung cancer, determine the probability of this patient suffering from adenocarcinoma, the probability of suffering from squamous cell carcinoma, the probability of suffering from large cell carcinoma, and the probability of suffering from other types of non-small cell lung cancer.

(b) Ten patients are randomly selected from the non-small cell lung cancer patients. Determine the probability that six patients have adenocarcinoma, three patients have squamous cell carcinoma, one patient has large cell carcinoma, and zero patients have other types of non-small cell lung cancer.

(c) Ten patients are randomly selected from the non-small cell lung cancer patients.
Determine the probability that four patients have adenocarcinoma.

(d) What is the probability distribution of

(b) and (c), and what is the relationship between these two distributions?

(e) Ten patients are randomly selected from the non-small cell lung cancer patients. Determine the expected value, variance, and standard deviation of the number of squamous cell carcinomas.