Question

for a certain class, the following data table compares how many students play an instrument or a sport. what is the probability that a student chosen randomly from the class plays a sport?
plays an instrument | does not play an instrument
plays a sport | 7 | 16
does not play a sport | 2 | 4

Explanation:

Step1: Find total number of students

First, we need to find the total number of students in the class. We add up all the values in the table: \(7 + 16 + 2 + 4\).
\(7+16 = 23\), \(2 + 4 = 6\), then \(23+6 = 29\). So total number of students is \(29\).

Step2: Find number of students who play a sport

Next, we find the number of students who play a sport. From the table, the number of students who play a sport is the sum of those who play a sport and an instrument, and those who play a sport but not an instrument. So that's \(7 + 16 = 23\).

Step3: Calculate the probability

The probability that a randomly chosen student plays a sport is the number of students who play a sport divided by the total number of students. So that's \(\frac{23}{29}\).

Answer:

\(\frac{23}{29}\)