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 or an instrument?

Explanation:

Find the total number of students

Using the Theoretical Probability knowledge point, we first determine the total number of outcomes (students in the class) by summing all the values in the two-way table:

$$ \text{Total} = 2 + 3 + 15 + 7 = 27 $$

Identify the favorable outcomes

We need to find the number of students who play a sport OR play an instrument. This includes:

• Students who play both: \(2\)
• Students who play a sport but not an instrument: \(3\)
• Students who play an instrument but not a sport: \(15\)

Summing these favorable outcomes:

$$ \text{Favorable} = 2 + 3 + 15 = 20 $$

Alternatively, we can subtract the students who do neither (7) from the total (27):

$$ \text{Favorable} = 27 - 7 = 20 $$

Calculate the probability

Using the Theoretical Probability formula, we divide the number of favorable outcomes by the total number of outcomes:

$$ P(\text{Sport or Instrument}) = \frac{\text{Favorable}}{\text{Total}} = \frac{20}{27} $$

Answer:

\(\frac{20}{27}\)