The probability of three events happening simultaneously, also known as the intersection of three events, can be calculated by multiplying the individual probabilities of each event. For example, if event A has a probability of 0.5, event B has a probability of 0.6, and event C has a probability of 0.7, the probability of all three events happening together is 0.5 * 0.6 * 0.7 = 0.21 or 21%.
The intersection of two events is the probability of both events happening together, while the intersection of three events is the probability of all three events happening together. In other words, the intersection of three events is the combined probability of all possible outcomes that satisfy all three events, whereas the intersection of two events is the combined probability of all possible outcomes that satisfy both events.
Yes, the intersection of three events can have a probability of 1 or 100%. This means that the three events are mutually exclusive, and the outcome must satisfy all three events. For example, if event A, event B, and event C cannot occur at the same time, the probability of all three events happening together is 1.
The inclusion-exclusion principle states that the probability of the union of two or more events is equal to the sum of their individual probabilities minus the sum of the probabilities of their intersections. This principle also applies to the intersection of three events, where the probability of all three events happening together is equal to the sum of the probabilities of each event minus the sum of the probabilities of each pair of events intersecting.
Yes, the intersection of three events can have a greater probability than each individual event. This can happen when the three events are not independent of each other, meaning that the outcome of one event affects the outcome of the other events. In this case, the combined probability of all three events happening together can be greater than the probability of each individual event.