Let A be the event that we choose an adult chaperone and let B be the event that we pick a male student. Then, we want to calculate the following probability.
[tex]P(A\cup B)[/tex]where the symbol between A and B means the union of events, which could be understood as "or". Using the properties of probability, we have
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]where the symbol on the right, between A and B, is the intersection, which can be understood as "and". Since we are going to pick only one person, it is impossible that we pick an adult chaperona and a male student. So,
[tex]P(A\cap B)=0[/tex]So we have
[tex]P(A\cup B)=P(A)+P(B)[/tex]Now, we want to calculate P(A) and P(B).
To calculate the probability of each event, we first count the number of possibilities that the event is true.
Note that since we have 6 adult chaperones, we have 6 possibilites such that the event A is true. Now, to calculate the probability of A, we simply divide this number by the total number of people on the bus (which is 50). So we get
[tex]P(A)=\frac{6}{50}[/tex]In the same manner, for event B, we have a total of 23 possibilities such that the event B is true. Then
[tex]P(B)=\frac{23}{50}[/tex]Finally, by replacing this values in the original expression, we have
[tex]P(A\cup B)=P(A)+(B)=\frac{6}{50}+\frac{23}{50}=\frac{29}{50}[/tex]