in a class of 21 students, 7 play an instrument and 8 play a sport. there are 8 students who do not play an…

Explanation:

Step1: Find number of students who play either instrument or sport

Total students = 21, students who play neither = 8. So number of students who play either instrument or sport is $21 - 8=13$.

Step2: Find number of students who play both instrument and sport

Let number of students who play instrument be $A = 7$, number of students who play sport be $B = 8$. Using the formula $n(A\cup B)=n(A)+n(B)-n(A\cap B)$, we have $13 = 7+8 - n(A\cap B)$. Solving for $n(A\cap B)$ gives $n(A\cap B)=7 + 8-13 = 2$.

Step3: Find number of students who play sport but not instrument

Number of students who play sport but not instrument is $n(B)-n(A\cap B)=8 - 2=6$.

Step4: Calculate the conditional - probability

The formula for conditional probability is $P(\text{not instrument}|\text{sport})=\frac{n(\text{sport and not instrument})}{n(\text{sport})}$. Substituting values, we get $P=\frac{6}{8}=\frac{3}{4}$.

Answer:

$\frac{3}{4}$