A widget inspector inspects 12 widgets and finds that exactly 3 are defective. Unfortunately, the widgets then get all mixed up and the inspector has to find the 3 defective widgets again by testing...

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A widget inspector inspects 12 widgets and finds that exactly 3 are defective. Unfortunately, the widgets then get all mixed up and the inspector has to find the 3 defective widgets again by testing widgets one by one.


(a) Find the probability that the inspector will now have to test at least 9 widgets.


(b) Find the probability that the inspector will now have to test at least 10 widgets.



Answered Same DayDec 26, 2021

Answer To: A widget inspector inspects 12 widgets and finds that exactly 3 are defective. Unfortunately, the...

David answered on Dec 26 2021
126 Votes
This problem can be easier in case if we find the complement of the given event and then
subtract is from 1 to get the required probability.
a) P(At least 9 widgets)
= P(X > 9)
= 1 – P(Less than 9 widgets)
= 1 – P(At most 8 widgets)
= 1 – P(X < 8)
Now,
P(At most 8 widgets to be...
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