Refer to Exercise 4.24 but now suppose there will be 75 units among which 45 will need to undergo a speed test and 30 will be tested for current flow. Find the probability that, among the four inspections assigned to the engineers, 3 will be speed tests and 1 will not, by using

(a) the binomial distribution as an approximation;

(b) the hypergeometric distribution.

Data From Exercise 4.24

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4.24 Suppose that, next month, the quality control division will inspect 30 units. Among these, 20 will undergo a speed test and 10 will be tested for current flow. If an engineer is randomly assigned 4 units, what are the probabilities that (a) none of them will need a speed test? (b) only 2 will need a speed test? (c) at least 3 will need a speed test?