Suppose that, for students who are enrolled in college algebra, 73 percent are freshmen, 48 percent are female, and 31 percent are female and are freshmen. Your answers below should be entered as decimals and rounded to three decimal places. Two students will be independently selected at random. What is the probability that both of the selected students will be female?
To find the probability that both selected students will be female, we need to multiply the probabilities of each event.
Given:
- Percentage of students who are freshmen = 73%
- Percentage of students who are female = 48%
- Percentage of students who are female and freshmen = 31%
Step 1: Convert the percentages to decimals.
- The percentage of freshmen = 73% = 0.73
- The percentage of female students = 48% = 0.48
- The percentage of female freshmen = 31% = 0.31
Step 2: Calculate the probability of selecting a female student.
P(female) = Percentage of female students = 0.48
Step 3: Calculate the probability of selecting a second female student, given that the first was female.
P(female|female) = Percentage of female freshmen = 0.31
Step 4: Multiply the probabilities to find the probability of both selected students being female.
P(both female) = P(female) * P(female|female)
P(both female) = 0.48 * 0.31 = 0.148
Step 5: Round the probability to three decimal places.
P(both female) ≈ 0.148
Therefore, the probability that both selected students will be female is approximately 0.148 or 14.8%.
To find the probability that both selected students will be female, you need to find the intersection (overlap) between the events "being a female" and "being a student." In this case, you are given that 48% of students are female and 31% of students are female freshmen.
To calculate the probability, you can multiply the probabilities of the two events occurring independently. Remember that when multiplying percentages, you need to convert them to decimals by dividing by 100.
First, let's calculate the probability of selecting a female student:
Probability of selecting a female student = 48% = 0.48 (after dividing by 100)
Next, let's calculate the probability of selecting a female freshman:
Probability of selecting a female freshman = 31% = 0.31 (after dividing by 100)
Now, multiply these probabilities together to find the probability of selecting two female students:
Probability of selecting two female students = Probability of selecting a female student × Probability of selecting a female freshman
= 0.48 × 0.31
= 0.1488
Rounding to three decimal places, the probability that both selected students will be female is approximately 0.149.