For the questions below, answer the following:

(i) name the discrete distribution involved,

(ii) identify the parameters and their values,

(iii) give the desired probability using theprobability mass function (pmf) formula, and

(iv) simplify the answer obtained using python.

3. It is known that 65% of mice inoculated with serum are protected from a specific disease. If 5 mice are inoculated, find the probability that a. None contracts the disease b. Fewer than 2 contracts the disease c. More than 3 contracts the disease

5. In testing a certain kind of truck tire over rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, find the probability that a. From 3 to 6 have blowouts b. Fewer than 4 have blowouts c. More than 5 have blowouts 6. An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. a. What is the probability that the first strike comes on the third well drilled? b. What is the probability that the third strike comes on the seventh well drilled? c. What is the mean and variance for the number of wells that must be drilled if the oil company wants to set up three producing wells?