1 answer:
First of all, we can observe that
So the expression becomes
This means that the expression is defined for every
Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask
Since we can't accept 3 as an answer, the actual solution set is
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You made a mistake with the probability , which should be
in the last expression, so to be clear I will state the expression again.
So we want to solve the following:
Conditioned on this event, show that the probability that her paper is in drawer , is given by:
(1) and
(2)
so we can say:
is the event that you search drawer
and find nothing,
is the event that you search drawer
and find the paper,
is the event that the paper is in drawer
this gives us:
Solution to Part (1):
if , then
,
this means that
as needed so part one is solved.
Solution to Part(2):
so we have now that if =
, we get that:
remember that:
this implies that:
so we just need to combine the above relations to get:
as needed so part two is solved.