if P(A)>0 then P(B'|A)=1-P(B|A)
so P(A intersect B')=P(A)P(B'|A)=P(A)[1-P(B|A)]
=P(A)[1-P(B)]
=P(A)P(B')
the definition of independent events is if P(A intersect B')=P(A)P(B')
that is the proof
Adlai Stevenson (Democratic Party) and Walter B. Jones (Independent)
Mexico was becoming independent
A-America B-boycott C-civil rights
To provide a chronological sequence of events, I would need specific events or a context to reference. Generally, chronological order means listing events from earliest to latest, such as event A occurring before event B, followed by event C. Please provide the specific events or context you have in mind for a more tailored response.
Operation Just Cause 1989; arrest of Manual Noriega, leader of Panama.
Yes.
Given two events, A and B, Pr(A and B) = Pr(A)*Pr(B) if A and B are independent and Pr(A and B) = Pr(A | B)*Pr(B) if they are not.
p(A and B) = p(A) x p(B) for 2 independent events p(A and B and ...N) = p(A) x p(B) x p(C) x ...x p(N) In words, if these are all independent events, find the individual probabilities if each and multiply them all together.
A and B are independent events if the probability of their intersection equals the product of their individual probabilities, which is mathematically expressed as P(A ∩ B) = P(A) * P(B). This means that the occurrence of event A does not affect the occurrence of event B and vice versa. If this equation holds true, then A and B can be considered independent.
.7
when the occurance of an event B is not affected by the occurance of event A than we can say that these events are not dependent with each other
Yes, when two probabilities are multiplied, it typically indicates a compound event, specifically in the context of independent events. This multiplication reflects the likelihood of both events occurring together. For instance, if you have two independent events A and B, the probability of both occurring is calculated by multiplying their individual probabilities: P(A and B) = P(A) × P(B). However, if the events are not independent, you would need to consider their relationship to determine the combined probability correctly.
the circles do not overlap at all.
first prove *: if A intersect B is independent, then A intersect B' is independent. (this is on wiki answers) P(A' intersect B') = P(B')P(A'|B') by definition = P(B')[1-P(A|B')] since 1 = P(A) + P(A') = P(B')[1 - P(A)] from the first proof * = P(B')P(A') since 1 = P(A) + P(A') conclude with P(A' intersect B') = P(B')P(A') and is therefore independent by definition. ***note*** i am a student in my first semester of probability so this may be incorrect, but i used the first proof* so i figured i would proof this one to kinda "give back".
P(A given B)*P(B)=P(A and B), where event A is dependent on event B. Finding the probability of an independent event really depends on the situation (dart throwing, coin flipping, even Schrodinger's cat...).
If two events are disjoint, they cannot occur at the same time. For example, if you flip a coin, you cannot get heads AND tails. Since A and B are disjoint, P(A and B) = 0 If A and B were independent, then P(A and B) = 0.4*0.5=0.2. For example, the chances you throw a dice and it lands on 1 AND the chances you flip a coin and it land on heads. These events are independent...the outcome of one event does not affect the outcome of the other.
apex XD 0.140.14