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This table shows how many students from two high schools attended a football game.
\begin{tabular}{|l|c|c|c|} \hline & Attended the game & \begin{tabular}{c} Did not attend \\ the game \end{tabular} & Total \\ \hline Westville & 60 & 90 & 150 \\ \hline North Beach & 110 & 90 & 200 \\ \hline Total & 170 & 180 & 350 \\ \hline \end{tabular}
A student is randomly selected. What is the probability that a student attended the game, given that the student is from North Beach? Round your answer to two decimal places.
To determine the probability that a student attended the game given that the student is from North Beach, we can use the concept of conditional probability. Here’s a step-by-step solution:
1. Identify the relevant data points. - Number of students from North Beach who attended the game: 110 - Total number of students from North Beach: 200
2. Formulate the probability. - The probability of an event occurring is calculated as the ratio of the number of successful outcomes to the total number of possible outcomes. - In this case, we want to find the probability that a student attended the game given that the student is from North Beach.
3. Calculate the probability. - Probability [tex]\( P( \text{Attended the game | From North Beach} ) \)[/tex] = [tex]\(\frac{\text{Number of students from North Beach who attended the game}}{\text{Total number of students from North Beach}}\)[/tex] - Substituting in the values: [tex]\( P( \text{Attended the game | From North Beach} ) = \frac{110}{200} \)[/tex]
4. Simplify the fraction and express it as a decimal. - [tex]\(\frac{110}{200} = 0.55\)[/tex]
5. Round the result to two decimal places. - The result is already in two decimal places: 0.55
Therefore, the probability that a student attended the game given that the student is from North Beach is [tex]\( 0.55 \)[/tex].
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