Sample spaces and events
Describing a random experiment by its sample space and its events, combining events (union, intersection, complement, mutual exclusivity), computing a probability by equiprobability and with the complement and union formulas.
- 27 cards
- 6 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Scenarios
- Understand
A few cards from the deck
Sample space of a random experiment: what is it?
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The set of all possible outcomes of the experiment, written Ω.
For one die roll, Ω = {1, 2, 3, 4, 5, 6}; for three coin tosses, Ω has 8 outcomes. Every probability calculation starts by writing Ω without leaving anything out.
A fair die is rolled. A: “the result is even”, B: “the result is at least 5”. What is P(A ∪ B)?
4/65/63/61/6
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4/6A = {2, 4, 6} and B = {5, 6}: A ∪ B = {2, 4, 5, 6}, that is 4 outcomes out of 6. Adding 3/6 + 2/6 gives 5/6 and counts the 6 twice; 1/6 is P(A ∩ B).
When all outcomes are equally likely, the probability of an event is the number of … cases divided by the number of … cases.
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When all outcomes are equally likely, the probability of an event is the number of favourable cases divided by the number of possible cases.
For a sum of 4 with two dice: 3 favourable pairs, (1,3), (2,2) and (3,1), out of 36 possible, that is 1/12. The denominator counts the equally likely outcomes, not the 11 sums.
Event: what is it?
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A subset of the sample space: the set of outcomes that satisfy a given condition.
“Rolling an even number” is the event {2, 4, 6}. An outcome is a single result; an event can gather several, or none, or all of them.