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Chapter 4: Problem 84

Of the 35 students in a class, 22 are taking the class because it is a major requirement, and the other 13 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? How does this probability compare to the probability that the first student is taking the class because it is a major requirement and the second is taking it as an elective?

Short Answer

Expert verified
The probability that the first student selected is taking the class as an elective and the second student is taking it as a major requirement is \( \frac{13}{35} * \frac{22}{34} \). The probability that the first student selected is taking the class as a major requirement and the second student is taking it as an elective is \( \frac{22}{35} * \frac{13}{34} \). Comparing these probabilities, we find that they are equal. This is because the total number of ways to pick a student doesn't change, whether we are looking at electives or majors first.

Step by step solution

01

Understand the concept of probability

Probability measures the likelihood of an event happening. It is calculated as the number of ways an event can happen, divided by the total number of outcomes. In this case, we are interested in the likelihood of picking a specific type of student from the class.
02

Determine the total number of students

In this problem, we have 35 students in total, of which 22 are taking the class because it is a major requirement, and 13 are taking it as an elective.
03

Calculate the probability of the first event

The probability that the first student picked is taking the class as an elective is the number of elective students divided by the total number of students. So, \( P(A) = \frac{13}{35} \).
04

Calculate the probability of the second event

After the first student, we have 34 students left. The probability that the second student picked is taking the class as a major requirement is the number of major students divided by the remaining total number of students. So, \( P(B) = \frac{22}{34} \). The joint probability is then \( P(A and B) = P(A) * P(B) =\frac{13}{35} * \frac{22}{34}\).
05

Compare the probabilities

Now, for the second scenario, where the first student is taking the class because it is a major requirement and the second student is taking it as an elective, we need to calculate this probability in the same way as in steps 3 and 4 but reversing the roles of A and B. Then, we just compare the values from both scenarios to find out which is greater or if they are equal.

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Most popular questions from this chapter

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