Question

Every school day, Mr. Kelley asks a randomly selected student to complete a homework

problem on the board. If the selected student received a "B" or higher on the last test, the
student may use a "pass," and a different student will be selected instead. Suppose that on
one particular day, the following is true of Mr. Kelley's students:
18 of 32 students have completed the homework assignment;
8 students have a pass they can use; and
6 students have a pass and have completed the assignment.
What is the probability that the first student Mr. Kelley selects has a pass or has completed
the homework assignment?

Answer 1

Let A be the event that the selected student has completed the homework assignment, and B be the event that the selected student has a pass.

P(A) = 18/32 (since 18 out of 32 students have completed the homework assignment)
P(B) = 8/32 (since 8 students have a pass they can use)
P(A and B) = 6/32 (since 6 students have a pass and have completed the assignment)

Now we can substitute these values into the formula:

P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 18/32 + 8/32 - 6/32
P(A or B) = 20/32

Therefore, the probability that the first student Mr. Kelley selects has a pass or has completed the homework assignment is 20/32 or 5/8.