Ten people apply for a job at Computer Warehouse. Five are...

Name: Problem 22, Chapter 5: Elementary Statistics a Step by Step Approach
Uploaded: 2023-03-09T11:50:55-08:00
Duration: 5 min 25 s
Channel: Sanchit Jain
Description: Ten people apply for a job at Computer Warehouse. Five are college graduates and five are not. If the manager selects 3 applicants at random, find the probability that all 3 are college graduates.

Ten people apply for a job at Computer Warehouse. Five are college graduates and five are not. If the manager selects 3 applicants at random, find the probability that all 3 are college graduates.

Key Concepts

Probability

Probability is a measure of how likely an event is to occur, often calculated as the ratio of the number of favorable outcomes to the total number of equally likely outcomes in the sample space. This concept is fundamental in determining the chance of an event happening in random experiments.

Combinatorics

Combinatorics is the branch of mathematics dealing with counting, arrangement, and selection of objects. It provides the tools and techniques needed to calculate the total number of possible outcomes and the number of favorable outcomes in problems involving random selection.

Combinations

Combinations refer to the method of selecting items from a larger pool where the order of selection does not matter. The combination formula, commonly represented as 'n choose k', is used to compute the number of ways to choose k items from a set of n, which is essential in computing probabilities in such random selection scenarios.

Sampling Without Replacement

Sampling without replacement means that once an item is selected, it is not returned to the pool for further selections. This concept is crucial in probability problems where each selection affects the outcome of future selections, thereby altering the total number of available choices.

Transcript

00:01 Hello students, we are going to write here.

00:03 In this particular question, 10 pupils apply for a job at computer warehouse.

00:08 5 are college graduates and 10, 5 are not.

00:12 So if i write here for this 10 pupil applied.

00:17 If i write here for this for a job, so 5 are graduates.

00:24 We need to write here for this.

00:26 This must be written as if i write here, 5 are not.

00:33 So basically if i write here for this, if the manager select three applicants at random, find the probability that all three are college graduates.

00:44 We need to write here for this.

00:47 So here x is a random variable which says that number of, we are going to write here for this, number of, graduates among randomly we need to write here for this so let's erase this to make it more clear among randomly randomly selected three people so basically if i write here for this this must be written as we need to write here here follows hyper geometric we need to write here for this distribution with parameters of so this must be written as having the parameters of n value is 10 and k value is 5 and if i write here for this this is an value as 3.

01:57 So basically if i write here for this, this must be written as so probability mass function for hypergeometric distribution is probability of random variable of x is equal to k.

02:12 This is k and if i write here for this this must be small k.

02:17 So this must be arranged to make it more clear.

02:22 Here, this must be capital k.

02:25 We need to write here, this must be capital k and small k, and this is capital n minus k, and small n minus k.

02:37 And if i write here for this, if i write here for this, this is divided by capital n and small n.

02:48 So basically what we need, probability of random variable x is equal to 3...

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