Question

A high school has 15 students who play only stringed instruments,20 students who play only brass instruments, and 5 students whodon't play any instruments. What is the probability that a randomlyselected student at this high school plays a stringed instrument or abrass instrument?5A15B20Find the indicated probability using the Venn diagram.P(AUB) = 2Be sure to simplify your answer!

Answer 1

P(A U B) = 7/8

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:

`\begin{gathered} P(A)=(15)/(40) \\ \text{ Simplifying:} \\ P(A)=(3)/(8) \end{gathered}`

Given that 20 students play only brass instruments, then the probability of event B is:

`\begin{gathered} P(B)=(20)/(40) \\ \text{ Simplifying:} \\ P(B)=(1)/(2) \end{gathered}`

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:

`P(A\cap B)=0`

Finally, the probability that a randomly selected student at this high school plays a stringed instrument or a brass instrument is:

`\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=(3)/(8)+(1)/(2)-0 \\ P(A\cup B)=(7)/(8) \end{gathered}`