Match each description with its symbolic representation.
1. p(a)
2. pab)
3. p(aub)
the probability that event a occurs
given the fact that event b occurs
the probability that either event a
or event b occurs
the probability that both events a
and b do not occur together, but either
may occur by itself
the probability that neither event a
or event b occurs
the probability that event a occurs
the probability that both event a
and event b occur
4. 1 - p(anb)
5. 1- p(aub)
6. p(aib)
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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

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