Question

The textbook basically says that the general addition rule is when A and B are two events in a probability experiment. The probability that either one of the events will occur is: P (A or B) = P (A) + P (B) – P (A and B). For example, if you take out a single card from a pack of cards, what is the probability that the card is either an ace or spade? Therefore, P(A) = 4/52, P (B) = 13/52, and P (A and B) = 1/52. P (A or B) = 4/52 + 13/52 – 1/52. P (A or B) = 4/13. Conditional Probability is the probability of one event (A) occurring with a relationship to another event (B). For example, in a sample of 40 vehicles, 18 are red, 6 are trucks, and 2 are both. Suppose that a randomly selected vehicle is red. What is the probability it is a truck? P(truck|red) = P (truck and red) / P (red). P (truck|red) = 2/40 = 18/40 = 2/18 = 1/9 or .11. So, if we must find the probability of an event which will occur given that another event has occurred, we will use conditional probability. If two events are mutually exclusive (no chance of things happening together) and you want to find the probability that an event A or B happens, we will use general addition rule.

"So we could use the general addition rule in the general election (in November elections) and use conditional probability in the primaries?"

Answer 1

As I am not sure about the term "primaries" but I can help you in finding why we will use additions and why or when we will use Conditional.

November election : As November election will be happened across the cointry, then if you want to just get the probabilities for individual results or combined results, then you can add the probabilities provided you are using "or" condition NOT "AND" for example, if you want to get the prob of getting votes in state A and state B then the probabilities will be multiplied giving you relatively lesser value compared to the OR condition. Now here also this can be happened if you think that the winning probabilities are independent of each other. Addition will give you the probability result of "winning in atleast one state" or similar situations.

Now coming to the Primary election, I have gathered information from google that Primary election can be happened in selected states, and under certain conditions, now in this case if you want to find a probability which is conditioned by some other factors then you HAVE TO use the conditional probabilities or Bayes theorem of multiple conditional probabilities. Sometimes it becomes so critical then you need to use Bayes network to solve the problem.

Hope I have answered the question and cleared the conceptual query.

Thanks !!