Suppose that, for students who are enrolled in college algebra, 78 percent are freshmen, 40 percent are female, and 28 percent are female and are freshmen. Your answers below should be entered as decimals and rounded to three decimal places.

(a) One student will be selected at random. What is the probability that the selected student will be a freshman or female (or both)?

.868

To find the probability that the selected student will be a freshman or female (or both), we need to consider the two events: being a freshman and being a female.

We are given the following information:
- 78 percent of the students enrolled in college algebra are freshmen, which means the probability of selecting a freshman is 0.780.
- 40 percent of the students enrolled in college algebra are female, which means the probability of selecting a female is 0.400.
- 28 percent of the students enrolled in college algebra are female and freshmen, which means the probability of selecting a student who is both female and a freshman is 0.280.

To calculate the probability of either event occurring, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Now we can substitute the values into the formula:

P(freshman or female) = P(freshman) + P(female) - P(freshman and female)
= 0.780 + 0.400 - 0.280

Calculating the expression:

P(freshman or female) = 0.900

Therefore, the probability that the selected student will be a freshman or female (or both) is approximately 0.900.