MAT EXAM TWO 230
This document proprietary Southern New Hampshire University. the problems within is to It and
may not posted any non-SNHU website.be on
Jacqueline Amoah
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Directions: Type your solutions into this document and sure show all steps for arriving be to at
your solution. Just giving a final number may not receive full credit.
P
ROBLEM
1
This question has 2 parts.
Part 1:
Suppose that and are events from a common sample space with F X P (F ) 0 and ≠P (X) ≠ 0.
(a)
Pro
v
e
that
P
(
X
)
=
P
(
X
F
)
P
(
F
)
+
P
(
X
F
¯)
P
(
F
¯
).
Hin
t:
Explain
wh
y
P
(
X
F
)
P
(
F
)
=
P X F ( ) another way writing the definition is of of conditional probability, then use and
that with the logic from the proof Theorem 4.1.1.of
P P P (X F ) (F ) = (X F ) is
true
because
we
want
to
get
all
probabilities
of
both
events
occurring
but
want
to
avoid
counting
those
events
that
have
already
been
counted.
When
the
intersection
of
the
probabilities
is
subtracted
we
take
away
those
