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.

1. From a lot of 10 missiles, four are selected randomly and fired. If the lot contains three defective missiles that will not fire, what is the probability that a. All 4 will fire? b. At most 2 will not fire? 2. The average number of field mice per acre in a 5-acre wheat field is estimated to be 12. Find the probability that fewer than 7 field mice are found on a given acre. 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 4. Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a specific airport, according to a Poisson process, at 6 per hour. a. What is the probability that exactly 4 small aircraft will arrive in 1 hour? b. What is the probability that at least 4 arrive in 1 hour? c. If we define a working day as 12 hours, what is the probability that 75 small aircraft will arrive during a working day?

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?