Random Sampling Examples
Example 1: A company has 500 products, and they want to randomly select 20 of them for quality testing. What is the probability of any single product getting selected?
Solution:
The chance of one-time selection is:
P = n/N
⇒ P = 20/500
⇒ P = 4%
Example 2: In a conference with 200 attendees, 50 will be randomly chosen for a survey. What is the probability that one attendee gets selected more than once?
Solution:
The probability of getting selected more than once is:
P = 1 – (1 – (1/N))n
⇒ P = 1 – (1 – (1/200))50
⇒ P ≈ 9.56%
Example 3: A university has 1,200 students, and they want to select 100 students for a survey using simple random sampling. What is the probability of any single student being chosen?
Solution:
The chance of one-time selection is:
P = n/N
⇒ P = 100/1200
⇒ P = 8.33%.
Example 4: In a raffle, 50 tickets are drawn from a pool of 1,000 tickets. What is the probability that a specific ticket does not get selected?
Solution:
The chance of a specific ticket not being selected is:
P = 1 – (n/N)
⇒ P = 1 – (50/1000)
⇒ P = 95%.
Example 5: A deck of 52 playing cards is shuffled, and 5 cards are drawn with replacement. What is the probability of drawing a specific card (e.g., the Ace of Spades) at least once?
Solution:
The probability of drawing a specific card at least once when drawing 5 cards with replacement is:
P = 1 – (1 – (1/N))n
⇒ P = 1 – (1 – (1/52))5
⇒ P ≈ 9.36%.
Important Maths related Links:
Random Sampling Method
Random Sampling is a method of probability sampling where a researcher randomly chooses a subset of individuals from a larger population. In this method, every individual has the same probability of being selected. The researcher aims to collect data from as large a portion as possible of this randomly chosen subset.
In the field of statistics, sampling serves as the technique for selecting a portion of the population to draw statistical inferences. This subset’s characteristics allow us to estimate the attributes of the entire population. In the realm of market research, sampling methods fall into two primary categories: Random or probability sampling and non-probability sampling.
This article discusses the specific category of probability sampling known as random sampling and its types, formulas, advantages, examples, etc.
Table of Content
- What is Random Sampling?
- Random Sampling Definition
- Types of Random Sampling
- Simple Random Sampling
- Systematic Random Sampling
- Stratified Random Sampling
- Cluster Random Sampling
- How to Perform Simple Random Sampling
- When to Use Random Sampling
- Random Sampling Formula
- Advantages of Simple Random Sampling
- Disadvantage of Simple Random Sampling
- Random Sampling vs Non-Probability Sampling
- Random Sampling Examples
- Practice Questions on Random Sampling
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