To find the probability that a student who plays an instrument does not play a sport, we first need to analyze the provided data table:
| | Plays a Sport | Does Not Play a Sport | |-----------------------|---------------|-----------------------| | Plays an Instrument | 2 | 10 | | Does Not Play an Instrument | 3 | 6 |
From the table, we identify the following numbers:
- Total students who play an instrument and also play a sport: 2
- Total students who play an instrument but do not play a sport: 10
Now, we calculate the total number of students who play an instrument:
\[ \text{Total who play an instrument} = \text{Plays a sport} + \text{Does not play a sport} = 2 + 10 = 12 \]
Next, we want to find the number of students who play an instrument and do not play a sport, which is 10.
The probability that a student who plays an instrument does not play a sport is given by the formula:
\[ P(\text{Does not play sport | Plays instrument}) = \frac{\text{Number who play instrument and do not play sport}}{\text{Total who play instrument}} \]
Substituting in the values:
\[ P(\text{Does not play sport | Plays instrument}) = \frac{10}{12} \]
Now, we can simplify this fraction:
\[ = \frac{5}{6} \]
Thus, the probability that a student who plays an instrument does not play a sport is \(\frac{5}{6}\).