Refer to Exercise 4.68 . Suppose that three students are randomly selected from the student body

step 1 Now, in this problem, there is a trick. So, this problem was earlier introduced where we were te

Refer to Exercise 4.68 . Suppose that three students are...

Key Concepts

Random Selection

Random selection refers to the process of choosing items from a larger set in such a way that every item has an equal chance of being picked. This concept is central to probability and ensures that the selected sample is representative of the population without bias.

Independent Events

Independent events are those whose outcomes do not affect each other. In probability theory, when events are independent, the occurrence of one event has no impact on the probability of the other events, allowing for simpler calculations.

Multiplication Rule for Independent Events

The multiplication rule states that for independent events, the probability of all events occurring together is equal to the product of their individual probabilities. This principle is widely used in probability calculations when determining the likelihood of multiple independent outcomes.

Transcript

00:01 Now, in this problem, there is a trick.

00:04 So, this problem was earlier introduced where we were telling that x will be the gpa.

00:10 So, x will be the score and which has a normal distribution, so and so.

00:16 But this time, they're asking a different question.

00:19 They're telling that suppose in this entire universe, we have chosen three students.

00:25 Now, now we want to know what is the probability that they will be given.

00:30 Getting more than 3 or less than 3 or whatever it is.

00:35 So first you understand that there is a trick.

00:37 It is no longer that x is greater than 3.

00:42 That is the only question.

00:44 Here the question is, if that number of the students out of 3, the students, all of them has to score more than 3.

00:54 So let us try to simplify.

00:56 So whenever there is a number of students and then some, probably we are trying to find first let us denote that the number of students with gpa greater than so now this can go like there can be out of those three zero students might have gotten greater than three or one student could have gotten greater than three well the other two couldn't do it could be two it could be three it won't be more than that.

01:37 So it is like 0 .1 .2 dot dot dot in.

01:42 Which distribution has a similar setup? 0 .1 .2.

01:45 Dot dot in.

01:46 Try to think.

01:47 Binomial, peugeot, there are many distributions.

01:50 Next, so we have one identity that is n is going to be three.

01:56 Now, what is this probability of why? probability of y is a particular student getting a gpa greater than be three.

02:06 That is, this is the probability for each of these, right? so, what is the probability that zero students will get gpa greater than three? or what is the probability that one student will get more than three? or two students will get more than three or three students...

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