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)
neyt question
asy or wip
turn it in

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

what the question so we can you out

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."