Example #1d: Two Events: Addition ('Or') LawIf A is an event and B is another event, then P(A or B) is the probability of either A occurring, orB occurring, or both occurring. 'Or' is commutative in the sense that P(A or B) = P(B or A). The following formula is used to find P(A or B): P(A or B)
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)
- Toss one fair coin (the coin has two sides, H and T).
- Toss one fair, six-sided die (the die has 1, 2, 3, 4, 5 or 6 dots on a side).
- Multiply the two numbers of outcomes.
The general probability addition rule for the union of two events states that P(A∪B)=P(A)+P(B)−P(A∩B) P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) , where A∩B A ∩ B is the intersection of the two sets. The addition rule can be shortened if the sets are disjoint: P(A∪B)=P(A)+P(B) P ( A ∪ B ) = P ( A ) + P ( B ) .
p(a,b) = the probability that event a and b happen at the same time. p(a|b) = the probability that event a happens due to the event b happens.
In probability, there's a very important distinction between the words and and or. And means that the outcome has to satisfy both conditions at the same time. Or means that the outcome has to satisfy one condition, or the other condition, or both at the same time.
Mathematically, the only difference is that P(A given B) is divided by P(B). Conceptually, P(A and B) is the probability that both A and B occur (the joint probability, or the probability of the intersection of A and B). P(A given B) is the probability that A occurs if B also occurs (conditional probability).
U(a,b) uniform distribution. equal probability in range a,b.
The probability of events A and B both occurring is the same as the probability of B and A both occurring. This has to do with conditional probability and the two probabilities are denoted p(A|B) and p(B|A) respectively.
Basic Probability Rules
- Probability Rule One (For any event A, 0 ≤ P(A) ≤ 1)
- Probability Rule Two (The sum of the probabilities of all possible outcomes is 1)
- Probability Rule Three (The Complement Rule)
- Probabilities Involving Multiple Events.
- Probability Rule Four (Addition Rule for Disjoint Events)
- Finding P(A and B) using Logic.
Probability OR: CalculationsThe formula to calculate the “or” probability of two events A and B is this: P(A OR B) = P(A) + P(B) – P(A AND B).
the probability that an event A does not happen is 100% minus the probability that A happens: P(Ac) = 100% - P(A). The complement rule can be derived from the axioms: the union of A and its complement is S (either A happens or it does not, and there is no other possibility), so P(AUAc) = P(S) = 100%, by axiom 2.
Mutually exclusive is a statistical term describing two or more events that cannot happen simultaneously. It is commonly used to describe a situation where the occurrence of one outcome supersedes the other.
A petabyte (PB) is a unit of digital information storage used to denote the size of data. It is equivalent to 1,024 terabytes or 1,000,000,000,000,000 bytes.
pb : peanut butter. pb&j : peanut butter and jelly.
PB is short for "personal best" and measures your top performance for a specific exercise, class or studio. Wear the Fiit device to track your stats during a workout.
Symbol for lead (plumbum).
| Acronym | Definition |
|---|
| BP | Beyond Petroleum (formerly British Petroleum) |
| BP | Blood Pressure (medical) |
| BP | Boiling Point |
| BP | Barometric Pressure |
