Question

In the con of the liberal arts college scenario, what is the probability that a randomly picked course is NOT an economics course?

a) Probability = 1/2

b) Probability = 1/3

c) Probability = 2/3

d) Probability = 1/6

Answer 1

The probability that a randomly picked course is not an economics course is 1 (or 100%) given that the listed disciplines at the college do not include economics, but the options provided in the question do not match this answer, indicating a possible error.

Step-by-step explanation:

The question provided by the student seems to be from a probability topic in Mathematics where the student is asked to find the probability that a randomly picked course is not an economics course. Assuming that the liberal arts college offers the listed disciplines of chemistry, math, English, psychology, sociology, history, nursing, physical education, art, and early childhood development as the only options, we would have a total of 10 different disciplines. Since the student is asking about the probability of not picking an economics course, and considering that economics is not stated as one of the disciplines, every picked course would not be an economics course. Therefore, the probability is 1, or 100%, that a randomly picked course is not an economics course. However, none of the provided answer options (a, b, c, d) match this probability, indicating that there may either be additional context needed that isn't provided, or there may be a typo.

Answer 2

The correct probability is d) Probability = 1/6.

Explanation:

To determine the probability that a randomly picked course is NOT an economics course in the liberal arts college scenario, we first need to understand the total number of courses and the number of economics courses. Let's denote the total number of courses as N and the number of economics courses as E.

The probability of randomly selecting a course that is NOT an economics course is given by the formula:

P(Not Economics) = 1 - P(Economics)^(*)

Now, the probability of selecting an economics course is given by the ratio of the number of economics courses to the total number of courses:

P(Economics) = E / N^(*)

Substituting this into the first formula, we get:

P(Not Economics) = 1 - (E / N)^(*)

According to the given options, the correct answer corresponds to 1/6, which implies that the probability of selecting a course that is NOT an economics course is 5/6. Therefore, the final answer is d) Probability = 1/6.

In conclusion, the probability of choosing a non-economics course in the liberal arts college scenario is 5/6, meaning there is a high likelihood of randomly selecting a course that is not in the economics department. This result is based on the fundamental principles of probability, where the complement of an event (in this case, not choosing economics) is equal to 1 minus the probability of the event itself