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Simple random sampling is a fundamental concept in statistics. It involves selecting a subset from a larger population in such a way that every possible subset of the same size has an equal chance of being chosen.
In simpler terms, imagine you have a bag of 100 colored marbles, and you need to pull out 10. If you close your eyes and pick any 10 marbles at random, you're conducting a simple random sample, assuming the marbles are indeed mixed well and every marble has an equal chance of being selected.
This method ensures that the sample is representative of the entire population, minimizing bias and helping researchers to make generalizations about the whole group. However, it's essential to adhere strictly to the principles of randomization to maintain the simplicity and fairness of this sampling method.

Probability refers to the likelihood that a certain event will occur. It's a fundamental element of both statistics and sampling techniques.
In sampling, probability is used to determine how likely it is that a particular individual will be chosen for the sample. The idea is to ensure a level of fairness and neutrality in selection so that results can be trusted.
For instance, when a professor rolls a die to decide which row to start the sampling process, she's employing a probability mechanism. However, for her sampling to be fair in a simple random sampling context,

• Every student should have an equal probability of being selected.
• The probability should not depend on seating arrangement.

Otherwise, some students or groups, like those in a certain seating location, might have a skewed chance, which violates the principles of fair probability in sampling.

Bias in sampling occurs when some members of a population are more likely to be included in the sample than others, leading to unrepresentative results.
This is an issue because it can distort findings and lead to conclusions that don't reflect the true characteristics of the population.
In the exercise example, the method introduces bias by selecting only a subset of rows, which inadvertently excludes many students based solely on their seating location. Having a number decided by a die does not eliminate this bias, as it still doesn't grant all individuals an equal chance to be part of the sample.
Some common causes of sampling bias include:

• Non-random seating or grouping.
• Inflexible selection method that doesn't cover all possibilities.
• Misplaced assumption that randomness has been achieved where it has not.

Awareness and careful design are key to minimizing such biases in the sampling process.