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Probability is a fundamental concept that helps us determine the likelihood of a specific outcome occurring. In Niki's case, we were given the probabilities of her receiving grades A, B, and C in her courses. This information can be expressed as probabilities of 0.30, 0.60, and 0.10 respectively for A, B, and C.
Understanding probability is essential when calculating expected values. Each grade value is associated with its probability, and these probabilities must always sum to 1, as they represent all possible outcomes for her grades.
A practical way to think of probability is:

• 0% means an event will not happen.
• 100% means an event will definitely happen.
• A 50% probability means the event will happen half of the time.

The Grade Point Average, or GPA, is a numerical representation of a student's average performance across all their courses. It is calculated using the weighted mean of the grades, where each letter grade is assigned a numerical value. In Niki’s case, A is worth 4, B is worth 3, and C is worth 2.
The GPA provides a standardized measure of academic achievement over a period, allowing for comparison. It's important for students because it reflects their academic progress and might be used for further education or job applications.
To calculate the GPA using the concept of expected value, we multiply each grade's value by the probability of receiving that grade, then sum these products. This gives us a single number that represents her average performance over the years.
As calculated, Niki’s GPA is 3.2, showing she predominantly achieved around a B grade level on average.

A random variable is a variable whose possible values are outcomes of a random phenomenon. In this scenario, Niki's grades are treated as random variables because they occur in uncertain conditions. Each course grade can be distinguished by different probabilities, something which is vital in calculating expected value.
Random variables can be:

• Discrete: with distinct, separate values like grades A, B, and C.
• Continuous: with values over a range, not relevant to Niki's grades.

In Niki's situation, treating grades as discrete random variables allows us to apply probability to future scenarios where outcomes can be predicted based on historical data. Understanding random variables helps us create models for expected value and thus improve decision-making based on past patterns.