Question

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 an instrument does not play a sport?
Plays an instrument Does not play an instrument
Plays a sport 2 3
Does not play a sport 10 6
Answer

Answer 1

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 \(\frac{5}{6}\).