Of the
53
students in a class,
33
are taking the class because it is a major requirement, and the other
20
are taking it as an elective. If two students are selected at random from this class, what is the probability that the first student is taking the class as an elective and the second is taking it because it is a major requirement? What is the probability that the first student is taking the class because it is a major requirement and the second student is taking the class as an elective?
Round your answers to four decimal places.
To calculate the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of possible outcomes. When choosing two students at random from a class of 53 students, there are 53 choices for the first student. Once the first student is chosen, there are 52 choices for the second student. Therefore, the total number of possible outcomes is 53 * 52 = 2756.
Now, let's calculate the probability that the first student is taking the class as an elective and the second is taking it because it is a major requirement.
Since there are 20 students taking the class as an elective and 33 taking it as a major requirement, the number of favorable outcomes is 20 choices for the first student and 33 choices for the second student. Therefore, the number of favorable outcomes is 20 * 33 = 660.
The probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 660 / 2756 = 0.2391
Therefore, the probability that the first student is taking the class as an elective and the second is taking it because it is a major requirement is approximately 0.2391.
Now, let's calculate the probability that the first student is taking the class because it is a major requirement and the second student is taking it as an elective.
The number of favorable outcomes is 33 choices for the first student and 20 choices for the second student. Therefore, the number of favorable outcomes is 33 * 20 = 660 (same as before).
The probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 660 / 2756 = 0.2391
Therefore, the probability that the first student is taking the class because it is a major requirement and the second student is taking it as an elective is also approximately 0.2391.