Let's start by organizing the given information about the homeroom class in a table.
S Last Name
T Last Name
Boys
6
8
Girls
4
11
A student is chosen at random. We are asked for the probability that the student is a girl or has a last name that starts with S. Let's name each one of these events!
lEventA: The student is a girl. EventB: The student's last name starts with S.Since there are girls whose last name starts with S these events are dependent. We will use the formula for the Probability of A or B.
Probability of A or B
P(AorB)=P(A)+P(B)-P(AandB)
We need to find each probability. This can be done by dividing the number of favorable outcomes by the total number of outcomes. Let's count these numbers from our table!
Girls
15
Students whose last name starts with S
10
Girls whose last name starts with S
4
Total number of students
29
We will now find the probability by dividing by the total number of students.
P(A)=& 15/29
P(B)=& 10/29
P(AandB)=& 4/29
Finally, we will substitute these values into the Probability of A or B formula and simplify.
