Question

Any certain high school 35 students play only string instruments 10 students play early brass instruments in five students play both there are also five students who play neither stringed nor brass Instruments what is the probability that a randomly selected student please either a string or a brass instrument

Answer 1

Step 1

Write out the expression of compound probability that will enable us solve the problem

`P(\text{AUB) = P(A) + P(B) - P(A and B)}`

Where,

P(AUB) = students that play both string and brass instruments =?

P(A) = Students that play only brass instruments = 10 +5 students that play both= 15

P(B) = Students that play only string instruments=35 + 5 stdents that play both = 40

P(A and B) = Students that do not play either brass and string instruments =5

Step 2

Find the probability that a randomly selected student plays either the string or brass instrument (P(AUB)) by substitution

P(AUB) = 15 + 40 -5 = 50 students

Step 3

Write an expression for the probability of an event occurring

`\text{Probability of event A occurring = }\frac{number\text{ of required events}}{\text{Total number of events}}`

Number of events = 50

Total number of events = 35 + 10 +5+5 = 55

Step 4

Get the required answer after substitution

`\begin{gathered} \text{Probability of P(AUB) = }(50)/(55)=0.9090909091 \\ \end{gathered}`

Hence the probability that a randomly selected student plays either a string or brass instrument is 0.9090909091