In a high school graduating class of 128 students, 52 are on...

Name: Problem 37, Chapter 9: Precalculus with Limits
Uploaded: 2021-05-20T15:21:46-08:00
Duration: 3 min 42 s
Channel: Michael Dunne
Description: In a high school graduating class of 128 students, 52 are on the honor roll. Of these, 48 are going on to college; of the other 76 students, 56 are going on to college. What is the probability that a student selected at random from the class is (a) going to college, (b) not going to college, and (c) not going to college and on the honor roll?

In a high school graduating class of 128 students, 52 are on the honor roll. Of these, 48 are going on to college; of the other 76 students, 56 are going on to college. What is the probability that a student selected at random from the class is (a) going to college, (b) not going to college, and (c) not going to college and on the honor roll?

Key Concepts

Basic Probability

This concept involves understanding probability as the ratio of the number of favorable outcomes to the total number of outcomes in a sample space. It is the foundational idea used to determine the likelihood of a particular event occurring.

Sample Space Partitioning

Partitioning the sample space means dividing the entire set of subjects into distinct, non-overlapping groups based on specific characteristics or events. In problems like these, the population is split into groups (such as those on the honor roll and those not on it) to simplify the calculation of probabilities for various events.

Complementary Probability

This concept refers to finding the probability of an event not occurring by subtracting the probability of the event from 1. It is useful when the probability of the complement (e.g., not going to college) is easier to compute or is directly needed.

Intersection of Events

The intersection of events involves identifying outcomes that satisfy more than one condition simultaneously, such as being on the honor roll and not going to college. This concept is crucial for analyzing combined events and calculating their joint probability.

Transcript

00:01 In this question, we're dealing with some students, some of which are on the honor roll, some are not, some are going to college, and we're going to answer some probabilities about these things.

00:10 So to start off, out of 128 students, 52 are on the honor roll, 48 of which are going to college.

00:17 So just to summarize some of our information, i always think this is important.

00:21 We have 52 on the honor roll, just abbreviate it like that, and we know 48 are going to college.

00:28 They didn't tell us this directly, but we know 48 are going to college.

00:34 Four are not.

00:37 Next, we have of the other 76.

00:39 So if 52 were on the on a roll, the other 76 they're speaking of, means 76 not on a roll.

00:48 We know this makes sense because if we add up 52 plus 76, we get 128, and that is all of the students.

00:56 So out of the 76, not on honor roll.

00:59 56 are going to college and the rest of them which would be 76 minus those 56 20 are not going to college.

01:10 So here's our basic data.

01:13 Now to answer some of these probability questions, the first one we have is that if a random student is selected, what is the probability that the student a is going to college? well, for this first one, we know the answer is going to be out of 128 because that is how many total.

01:29 Students there are.

01:31 And how many are going to college? well, we have 48 going to college out of the honor will group.

01:36 We have 56 going to college out of the non -honor rule group.

01:41 So if we add those up with a 48 plus a 56, again, the total number going to college, we do get 104.

01:48 So the probability that a random student is going to college is 104 out of 128.

01:54 This could be simplified or turned into a decimal, but that is the basic probability...

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