Mutually exclusive events cannot occur together: every pair has an empty intersection. If one event occurs, the others do not. When such events are also exhaustive, their union covers every possible outcome. section 5.3.2 section 5.2
For mutually exclusive events, the probability of one event or another is the sum of their probabilities. For an exhaustive collection, that sum equals 1 because one of the events must occur. section 5.3.2 section 5.10
Quantized weights in Statsville
Partition adult weights into S1 (less than 60 kg), S2 (between 60 and 90 kg), and S3 (more than 90 kg). These ranges are mutually exclusive and exhaustive. Their probabilities are 0.25, 0.50, and 0.25, so P(S1 or S2 or S3) = 1. section 5.2 section 5.3.2
The same structure extends to continuous variables. Infinitesimal intervals do not overlap, collectively cover the domain, and replace the discrete probability sum with an integral of the probability density. section 5.6
Table 5.2 Probability distribution for quantized weights of Statsville adults
| S1: Less than 60 kg |
S2: Between 60 and 90 kg |
S3: More than 90 kg |
|---|---|---|
| p(X = 1) = 25,000/100,000 = 0.25 | p(X = 2) = 50,000/100,000 = 0.5 | p(X = 3) = 25,000/100,000 = 0.25 |
Browse the probability table for the three mutually exclusive weight ranges and their numerical probabilities. section 5.2
