Find p(a|a^c)
a.1
b.0
c.1/2
d. unknown

If has occurred, then cannot occur, so the probability is 0.

This follow directly from the definition of conditional probability:

but and are disjoint, so the probability of their intersection is 0.

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)