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The given two-way table shows the number of passengers, by type, on the Ferris wheel at an amusement park for its first two runs on a Sunday morning.

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & First Run & Second Run & Total \\
\hline
Children & 122 & 146 & 268 \\
\hline
Adults & 183 & 219 & 402 \\
\hline
Total & 305 & 365 & 670 \\
\hline
\end{tabular}

Based on the data in the table, what is the value of [tex]\( P(\text{Adult}|\text{Second run}) \)[/tex] rounded to the nearest thousandth?

A. 0.6
B. 0.327
C. 0.545
D. 0.4


Sagot :

To solve for [tex]\( P(\text{Adult}|\text{Second run}) \)[/tex], we need to determine the probability that a randomly selected passenger from the second run is an adult.

Let's follow these steps:

1. Identify the number of adults on the second run:
From the table, the number of adults on the second run is 219.

2. Identify the total number of passengers on the second run:
From the table, the total number of passengers on the second run is 365.

3. Calculate the probability:
The probability [tex]\( P(\text{Adult}|\text{Second run}) \)[/tex] is given by the ratio of the number of adults on the second run to the total number of passengers on the second run:
[tex]\[ P(\text{Adult}|\text{Second run}) = \frac{\text{Number of adults on second run}}{\text{Total number of passengers on second run}} = \frac{219}{365} \][/tex]

4. Round the result to the nearest thousandth:
The fraction [tex]\(\frac{219}{365}\)[/tex] evaluates to approximately 0.6 when rounded to the nearest thousandth.

Hence, the value of [tex]\( P(\text{Adult}|\text{Second run}) \)[/tex], rounded to the nearest thousandth, is 0.6. Therefore, the correct answer is:

A. 0.6