To determine the probability that a randomly chosen student from the class plays a sport, we need to follow these steps:
1. Identify the number of students who play a sport:
- Number of students who play a sport and play an instrument: [tex]\(6\)[/tex]
- Number of students who play a sport and do not play an instrument: [tex]\(8\)[/tex]
Therefore, the total number of students who play a sport is:
[tex]\[
6 + 8 = 14
\][/tex]
2. Identify the total number of students in the class:
- Number of students who play a sport and play an instrument: [tex]\(6\)[/tex]
- Number of students who play a sport and do not play an instrument: [tex]\(8\)[/tex]
- Number of students who do not play a sport but play an instrument: [tex]\(13\)[/tex]
- Number of students who do not play a sport and do not play an instrument: [tex]\(3\)[/tex]
Therefore, the total number of students in the class is:
[tex]\[
6 + 8 + 13 + 3 = 30
\][/tex]
3. Calculate the probability that a randomly selected student plays a sport:
The probability is given by the ratio of the number of students who play a sport to the total number of students in the class. So we have:
[tex]\[
\text{Probability} = \frac{\text{Number of students who play a sport}}{\text{Total number of students in the class}} = \frac{14}{30}
\][/tex]
4. Simplify the fraction (if needed):
In this case, [tex]\(\frac{14}{30}\)[/tex] can be simplified by dividing both the numerator and the denominator by 2:
[tex]\[
\frac{14}{30} = \frac{14 \div 2}{30 \div 2} = \frac{7}{15}
\][/tex]
5. Convert the fraction to a decimal:
To understand the fraction in decimal form, we can perform the division:
[tex]\[
\frac{7}{15} \approx 0.4667
\][/tex]
Therefore, the probability that a randomly chosen student plays a sport is approximately [tex]\(0.4667\)[/tex].
So, the final answer is that the probability that a student chosen randomly from the class plays a sport is [tex]\( \frac{14}{30} = 0.4667 \)[/tex].
