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