Answer:
i) P(A) ; The probability that event A occurs
ii) P(AB) ; The probability that both event A and event B occur
iii) P(AUB) ; The probability that either event A or event B occurs
iv) 1 - P(ANB) ; The probability that both events A and B do not occur together, but either may occur by itself
v) 1- P(AUB) ; The probability that neither event A or event B occurs
vi) P(AIB) ; The probability that event A occurs given the fact that event B occurs
Step-by-step explanation:
i)
P(A) simply represents the probability that an event A will occur. This event could be passing an examination, having snow in summer, arriving to work on time and so forth.
ii)
P(AB) is simply the probability that both event A and event B do occur. This is usually given by the product of the individual probabilities. Event A could be rolling a 6 in one throw of a fair die while B could be the event that a fair coin lands heads in a single toss.
iii)
P(AUB) refers to the probability that either event A or event B occurs. This is read out as the probability of A union B. This is usually given by the sum of the individual probabilities.
iv)
1 - P(ANB) is the probability that both events A and B do not occur together, but either may occur by itself. P(ANB) is the probability that both events A and B occur together. This is read out as the probability of A intersection B. Therefore implying that 1 - P(ANB) is simply the probability that either event A or B occurs but A and B can not occur together.
v)
1- P(AUB) refers to the probability that neither event A or event B occurs. Earlier we defined P(AUB) as the probability that either event A or event B occurs. 1- P(AUB) simply the complement of P(AUB).
vi)
P(AIB) refers to the probability that event A occurs given the fact that event B occurs. This is a conditional probability event which evaluates the likelihood of an event A occurring given that an associated event B has already occurred
