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9. A special task force suspects that some manufacturing companies are in violation
of the national pollution regulations with regard to dumping a certain type of toxic material.
There are 37 firms that are under suspicion, but all cannot be inspected.
Suppose that 12 of the firms are in violation.
a. What is the probability that inspection of 14 firms finds 2 violations?
b. What is the probabilit that inspection of 12 firms finds 3 violations?
c. What is the probability that inspection of 17 firms finds 6 violations?
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In this my post, I will explain you on how to solve part (a) in all details.
Aftet that, you will be able to solve (b) and (c) on your own.
Part (a)
The total number of the firms to check is 37.
It is known (and given) that 12 firms are violators (hence, 37-12 = 25 are not violators).
The strategy is to check 14 firms at a time.
What is the probability to find 2 violators using this strategy ?
The total number of all possible subsets of 14 firms among 37 firms is total = = 6107086800.
It is a cosmic magnitude number; but you can easily find it in one click
using Excel standard function combin for the number of combinations.
The "favorable" configurations in this problem are THESE: (2 violators,12 non-violators): 2 + 12 = 14.
The number of such "favorable" combinations in this problem is
= 66*5200300 = 343219800.
Now the probability under the problem's question is P = = = 0.056200249. ANSWER
Part (a) is complete.
Solve other parts similarly.