In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student who plays a sport also plays an instrument?

Plays an instrument Does not play an instrument
Plays a sport 4 7
Does not play a sport 2 8
Answer

1 answer

To find the probability that a student who plays a sport also plays an instrument, we can use the data provided in the table.

Here is the correct interpretation of the provided data:

  • Students who play both an instrument and a sport: 4
  • Students who play a sport but do not play an instrument: 7

First, we need to find the total number of students who play a sport. This is done by adding the number of students who play both an instrument and a sport and those who only play a sport:

\[ \text{Total who play a sport} = \text{Plays instrument and sport} + \text{Plays sport, does not play instrument} = 4 + 7 = 11 \]

Next, we want to calculate the probability that a student who plays a sport also plays an instrument. This probability is represented as:

\[ P(\text{Plays instrument} | \text{Plays sport}) = \frac{\text{Number of students who play both}}{\text{Total number of students who play a sport}} = \frac{4}{11} \]

Thus, the probability that a student who plays a sport also plays an instrument is:

\[ \frac{4}{11} \]