I have a probability question and have read through the threads but am still confused as I am not very mathematically inclined (I have trouble understanding/following the equations used in previous threads). Basically I want to combine multiple probabilities to get an overall probability. Example: say I have four variables related to passing a course or failing a course and have individual probabilities related to each of these variables for each student. So, for student 1, variable a results in a 0.47, variable b 0.6, variable c 0.2, and variable d 0.8 probability of passing the course. How would I calculate the overall probability that they pass the course? I’ve read that multiplying the probability of each variable will result in a combined (i.e., overall) probability but I feel like it can’t be that simple. Am I overthinking this? Any help is much appreciated!
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2How exactly do the variables relate to the outcome? For instance, is each variable the probability of passing one of four assessments, and the student needs to pass all/at least one/at least three of these assessments? Options like these will make a difference in how the probabilities can be combined. – Stephan Kolassa May 19 '21 at 15:06
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Variables are characteristics related to the student that theoretically impact the outcome of passing a course. For example, number of hours studied or socioeconomic status or number of hours working at a part-time job. My example is mainly for illustrative purposes so I can wrap my head around a simpler case before trying to tackle my own, more complex data. – plantguy May 19 '21 at 15:22
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So it's fair to say that you have $p(y | a)$, $p(y | b)$, $p(y | c)$, and $p(y | d)$, and you'd like to compute $p(y | a, b, c, d)$? – Arya McCarthy May 19 '21 at 15:32
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Your toy example is missing information, such as the probability of passing with none of these (do some make things worse?), and a model for how they interact in combination (for example additively on the log-odds) – Henry May 19 '21 at 15:40
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@AryaMcCarthy Yes, I think so. My aim would be an 'average' probability across variables so to speak. – plantguy May 19 '21 at 15:41
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Does this answer your question? Proper way to combine conditional probability distributions of the same random variable conditioned on a discrete variable ? (based on assumptions) – Arya McCarthy May 19 '21 at 16:00