This table shows how many sophomores and juniors attended two school events.
\begin{tabular}{|l|l|l|l|}\hline & Jazz band concert & Volleyball game & Total \\\hline Sophomore & 35 & 42 & 77 \\\hline Junior & 36 & 24 & 60 \\\hline Total & 71 & 66 & 137 \\\hline\end{tabular}
What is the probability that a randomly chosen person from this group is a sophomore and attended the volleyball game?
Round your answer to two decimal places.
A. 0.26
B. 0.56
C. 0.31
D. 0.48
Answer (2)
Find the number of sophomores who attended the volleyball game: 42.
Find the total number of people: 137.
Calculate the probability: 137 42 ≈ 0.3066 .
Round to two decimal places: 0.31 .
Explanation
Understand the problem We are given a table that shows the number of sophomores and juniors who attended a jazz band concert and a volleyball game. We want to find the probability that a randomly chosen person from this group is a sophomore and attended the volleyball game.
Identify the number of sophomores who attended the volleyball game From the table, we can see that there are 42 sophomores who attended the volleyball game.
Identify the total number of people The total number of people is 137.
Calculate the probability To find the probability that a randomly chosen person is a sophomore and attended the volleyball game, we divide the number of sophomores who attended the volleyball game by the total number of people: 137 42 ≈ 0.306569343
Round the probability Rounding the probability to two decimal places, we get 0.31.
Examples
This type of probability calculation is useful in many real-world scenarios. For example, if a school administrator wants to know the probability that a student selected at random is a sophomore who attended the volleyball game, this calculation would provide that information. This can help the administrator understand student interests and participation in school events. Another example could be in market research, where you want to determine the probability that a randomly selected customer is in a certain demographic and purchased a specific product.
To find the probability that a randomly chosen person is a sophomore who attended the volleyball game, we divide the number of sophomores (42) by the total number of people (137). This results in a probability of approximately 0.31. Therefore, the correct answer is C. 0.31.
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