(1) Three items are selected at random from a manufacturing process & classified defective or non-defective. A defective item is designated a success. Assume $25\%$ of the production is defective. Let $X$ be the number of successes, let $N$: non-defective, $D$: defective.
When I use the formula $P(X=2)=b(2;3,0.25)=9/64$. But when I use $P(NDD)=(3/4)(1/4)(1/4)=3/64$. What is wrong here?
(2) In a certain rural community "$30\%$ of wells are impure" is merely a conjecture put forth by the area water board.Suppose $10$ wells are randomly selected & $6$ are found to contain the impurity.
By using the formula $P(X=6)=0.0367$, please explain which result you compare with the result $0.0367$ to conclude that the conjecture is unlikely.