Respuesta :
Solution
Step 1
Write out the expression of compound probability that will enable us solve the problem
[tex]P(\text{AUB) = P(A) + P(B) - P(A and B)}[/tex]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
[tex]\text{Probability of event A occurring = }\frac{number\text{ of required events}}{\text{Total number of events}}[/tex]Number of events = 50
Total number of events = 35 + 10 +5+5 = 55
Step 4
Get the required answer after substitution
[tex]\begin{gathered} \text{Probability of P(AUB) = }\frac{50}{55}=0.9090909091 \\ \end{gathered}[/tex]Hence the probability that a randomly selected student plays either a string or brass instrument is 0.9090909091
