Answer
P(A U B) = 7/8
Step-by-step explanation
Events
• A: a student plays only stringed instruments
,
• B: a student plays only brass instruments
The total number of students is 15 + 20 + 5 = 40
Given that 15 students play only stringed instruments, then the probability of event A is:
[tex]\begin{gathered} P(A)=\frac{15}{40} \\ \text{ Simplifying:} \\ P(A)=\frac{3}{8} \end{gathered}[/tex]
Given that 20 students play only brass instruments, then the probability of event B is:
[tex]\begin{gathered} P(B)=\frac{20}{40} \\ \text{ Simplifying:} \\ P(B)=\frac{1}{2} \end{gathered}[/tex]
Each student plays only one of the instruments, then the probability that a student plays both instruments is zero. Considering events A and B, this is equivalent to:
[tex]P(A\cap B)=0[/tex]
Finally, the probability that a randomly selected student at this high school plays a stringed instrument or a brass instrument is:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=\frac{3}{8}+\frac{1}{2}-0 \\ P(A\cup B)=\frac{7}{8} \end{gathered}[/tex]
