Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Drag each number to the correct location on the table.
Complete a two-way frequency table using the given probability values.

[tex]\[
\begin{array}{l}
P(A \mid X) = \frac{40}{92} \\
P(B) = \frac{78}{160} \\
\begin{array}{llllllll}
42 & 68 & 82 & 52 & 78 & 26 & 92 & 40
\end{array}
\end{array}
\][/tex]

\begin{tabular}{|c|c|c|c|}
\hline
& [tex]$X$[/tex] & [tex]$Y$[/tex] & Total \\
\hline
A & & & \\
\hline
[tex]$B$[/tex] & & & \\
\hline
Total & & & 160 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To complete the two-way frequency table using the given probabilities and tabulated values, we have to appropriately place the given numbers [tex]\(42, 68, 82, 52, 78, 26, 92, 40\)[/tex].

Let's place these numbers step-by-step.

First, we have:
[tex]\[ P(A \mid X) = \frac{40}{92} \][/tex]
This information tells us that [tex]\( A \cap X \)[/tex] (the number of outcomes that are both A and X) is 40 and the total number of outcomes in X is 92. Thus:

- [tex]\( A_X = 40 \)[/tex]
- [tex]\( X_{total} = 92 \)[/tex]

Next, we know:
[tex]\[ P(B) = \frac{78}{160} \][/tex]
We are given the total number of outcomes is 160.

So:
- [tex]\( B_{total} = 78 \)[/tex]
- [tex]\( A_{total} = 160 - 78 = 82 \)[/tex]

Similarly, because the total is divided into X and Y:
- [tex]\( Y_{total} = 160 - 92 = 68 \)[/tex]

Now, let's find other missing values:

1. Since [tex]\( A_X = 40 \)[/tex] and [tex]\( A_{total} = 82 \)[/tex]:
- [tex]\( A_Y = A_{total} - A_X = 82 - 40 = 42 \)[/tex]

2. We know [tex]\( B_{total} = 78 \)[/tex] and [tex]\( X_{total} = 92 \)[/tex]:
- [tex]\( B_X = X_{total} - A_X = 92 - 40 = 52 \)[/tex]

3. Finally, knowing [tex]\( B_{total} = 78 \)[/tex] and [tex]\( B_X = 52 \)[/tex]:
- [tex]\( B_Y = B_{total} - B_X = 78 - 52 = 26 \)[/tex]

Now, let's place all these values into the table.

[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & X & Y & Total \\ \hline A & 40 & 42 & 82 \\ \hline B & 52 & 26 & 78 \\ \hline Total & 92 & 68 & 160 \\ \hline \end{tabular} \][/tex]

Here's how the numbers are distributed into the table:
- [tex]\( 40 \)[/tex] is placed at [tex]\( A \cap X \)[/tex]
- [tex]\( 42 \)[/tex] is placed at [tex]\( A \cap Y \)[/tex]
- [tex]\( 52 \)[/tex] is placed at [tex]\( B \cap X \)[/tex]
- [tex]\( 26 \)[/tex] is placed at [tex]\( B \cap Y \)[/tex]
- [tex]\( 92 \)[/tex] is the total of column X
- [tex]\( 68 \)[/tex] is the total of column Y
- [tex]\( 82 \)[/tex] is the total of row A
- [tex]\( 78 \)[/tex] is the total of row B
- The total number of observations is 160

Thus the table is complete and consistent with the given probabilities and values.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.