[50 Points] At a certain high school, 25 students play only stringed instruments, 15 students play only brass instruments, and 5 students play both. There are also 5 students who play neither stringed nor brass instruments. what is the probability that a randomly selected student plays either a string or brass instrument?
The notation A U B represents the set of people in set A, set B, or both sets at the same time. The U refers to "union". A union of two or more sets just basically has us combine those sets together to form a larger set (toss out any duplicates).
A = set of stringed instrument players
B = set of brass instrument players
A U B = set of stringed instrument players or brass instrument players
n(A U B) = 25 + 5 + 15
n(A U B) = 45
---------------
There are 45 students who play either instrument or both.
This is out of 5+25+5+15 = 50 total
Divide the two values: 45/50 = 9/10 = 0.90
This is the probability of selecting a student who plays either instrument.
