## Related questions with answers

A population of $600$ semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the following table. A wafer is chosen at random from the population.

$\begin{array}{crr} \hline \textbf{Lot} & \textbf{Conforming} & \textbf{Nonconforming}\\ \hline \textbf{A} & 88\hspace{20pt} & 12\hspace{30pt}\\ \textbf{B} & 165\hspace{20pt} & 35\hspace{30pt}\\ \textbf{C} & 260\hspace{20pt} & 40\hspace{30pt}\\ \hline \end{array}$

$\textbf{a.}\hspace{10pt}$ What is the probability that a wafer is from Lot A?

$\textbf{b.}\hspace{10pt}$ What is the probability that a wafer is conforming?

$\textbf{c.}\hspace{10pt}$ What is the probability that a wafer is from Lot A and is conforming?

$\textbf{d.}\hspace{10pt}$ Given that the wafer is from Lot A, what is the probability that it is conforming?

$\textbf{e.}\hspace{10pt}$ Given that the wafer is conforming, what is the probability that it is from Lot A?

$\textbf{f.}\hspace{10pt}$ Let $E_1$ be the event that the wafer comes from Lot A, and let $E_2$ be the event that the wafer is conforming. Are $E_1$ and $E_2$ independent? Explain.

Solution

Verified**(a)**

To determine the probability that a wafer is from Lot A we will use this equation below.

$P(A)=\frac{\text{Number of a wafer from Lot A}}{\text{Total number of a population of semiconductor wafers}}$

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