Question

The probability that a freshman at a certain college takes an introductory statistics class is 0.21. What is the probability that a randomly selected freshman from this college does not take an introductory statistics class

Answer 1

To solve this problem, we'll use the principle that the sum of the probabilities of all possible outcomes in a probability space is 1. The probability space here consists of two outcomes for a randomly chosen freshman: either they take an introductory statistics class or they do not take it.

We are given the probability of one of these outcomes: the probability that a freshman takes an introductory statistics class (let's call this event "takes statistics") is 0.21.

Let's denote the probability that a freshman does not take an introductory statistics class (let's call this event "does not take statistics") as P(does not take statistics).

By the principle mentioned, we have:
P(takes statistics) + P(does not take statistics) = 1

We can rearrange this to solve for P(does not take statistics):
P(does not take statistics) = 1 - P(takes statistics)

Substitute the given probability into our equation:
P(does not take statistics) = 1 - 0.21

When we calculate this, we get:
P(does not take statistics) = 0.79

Thus, the probability that a randomly selected freshman from the college does not take an introductory statistics class is 0.79, which means a 79% chance when rounded to two decimal points.

Answer 2

`P(A) = 0.21`

We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:

`P(A') = 1-P(A)`

Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:

`P(A')=1-0.21= 0.79`

Explanation:

For this problem we know that the probability that a freshman at a certain college takes an introductory statistics class is 0.21, let's define of interest as A and we can set the probability like this:

`P(A) = 0.21`

We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:

`P(A') = 1-P(A)`

Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:

`P(A')=1-0.21= 0.79`