[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?

Explanation:

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.