The computer department at your school has received a...

Name: Problem 19, Chapter 12: Higher Level Mathematics
Uploaded: 2020-05-13T17:26:51-08:00
Duration: 2 min 8 s
Channel: Julian Wong
Description: The computer department at your school has received a shipment of 25 printers, of which 10 are colour laser printers and the rest are black-and-white laser models. Six printers are selected at random to be checked for defects. What is the probability that a) exactly 3 of them are colour lasers? b) at least 3 are colour lasers?

The computer department at your school has received a shipment of 25 printers, of which 10 are colour laser printers and the rest are black-and-white laser models. Six printers are selected at random to be checked for defects. What is the probability that a) exactly 3 of them are colour lasers? b) at least 3 are colour lasers?

The computer department at your school has received a shipment of 25 printers, of which 10 are colour laser printers and the rest are black-and-white laser models. Six printers are selected at random to be checked for defects. What is the probability that
a) exactly 3 of them are colour lasers?
b) at least 3 are colour lasers?

Key Concepts

Hypergeometric Distribution

This concept applies to scenarios where a fixed number of items is selected from a finite population without replacement. The hypergeometric distribution is used to compute probabilities when sampling, especially when the population is divided into two distinct groups (such as defective and non?defective, or in this case, color and black?and?white printers) and the interest lies in the number of successes drawn from one group.

Combinatorial Analysis

Combinatorial analysis involves counting the number of ways to choose items from a set when order does not matter. In probability problems like this, combinations are used to determine the number of ways to select a specific number of items from a group and the total number of ways to select items from the entire population, which is critical for calculating probabilities accurately.

Sampling Without Replacement

This concept refers to the process by which items are selected from a population and are not returned before the next selection. The lack of replacement means that the probabilities change on each draw. This is a key condition for the applicability of the hypergeometric distribution, as the outcome of each draw influences the next, in contrast to independent sampling with replacement.

Probability Calculation for 'Exactly' and 'At Least' Events

Probability calculations often differentiate between scenarios where a condition is met exactly a specific number of times and scenarios where it is met a minimum number of times ('at least'). When computing 'exactly' events, one uses combinatorial methods to select the precise number of interest, while 'at least' events typically involve summing the probabilities of several exact outcomes, ensuring all possibilities that meet the condition are included.

Transcript

Please give Ace some feedback