Packet 5: Bonus 13
All probability spaces have the property that the result of this operation applied to any number of events within the space is also in the space. For 10 points each:
[10m] Name this operation that, when applied to two sets, returns the set of all elements that are in the first set or the second set. This operation is expressed with the “cup” symbol, as opposed to a similar one expressed with a “cap”.
ANSWER: union
[10e] The union of multiple different events can be visualized using this figure. For situations with two possible events, this figure is commonly drawn as two overlapping circles.
ANSWER: Venn diagram
[10h] The probability of the union of two events can be calculated as the sum of the probabilities of each event minus the probability of their intersection, according to the n = 2 case of this combinatorics “principle” sometimes referred to with a three-letter acronym.
ANSWER: principle of inclusion–exclusion [or the inclusion–exclusion principle; accept PIE]
<Math — Kevin Qiu> | SHOW-ME Four Packet 5
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 26 | 16.15 | 89% | 65% | 8% |
Conversion
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| Rube Goldberg XIX | 11/20/2025 | ✓ | 16 | 14.38 | 88% | 50% | 6% |
| SHOW-ME Four Nationwide HS | 11/20/2025 | ✓ | 5 | 22.00 | 100% | 100% | 20% |
| SPOOKY IX | 11/20/2025 | ✓ | 5 | 16.00 | 80% | 80% | 0% |