in a class of 30 students, 5 play an instrument and 9 play a sport. there are 18 students who do not play an…

Explanation:

Step1: Find number of students who play both

Let (A) be the set of students who play an instrument and (B) be the set of students who play a sport. We know (n(A\cup B)=5 + 9 - n(A\cap B)). Also, number of students who do not play an instrument or a sport is (18), so (n(A\cup B)=30 - 18=12). Then (12 = 5+9 - n(A\cap B)), so (n(A\cap B)=2).

Step2: Find number of students who play sport but not instrument

Number of students who play a sport but not an instrument is (n(B)-n(A\cap B)=9 - 2 = 7).

Step3: Calculate the probability

The probability that a student who plays a sport does not play an instrument is (\frac{\text{Number of students who play sport but not instrument}}{\text{Number of students who play sport}}). So the probability (P=\frac{7}{9}).

Answer:

(\frac{7}{9})