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b) asked for pmf
P_x (8/14)^2 x=-2
(4/14)*(8/14) x=1
(4/14)^2 x=2

What type of math is this? Algebra 1?

Honestly, I have no clue.

lol

probability

sampling with or without replacement?

didn't say anything about replacement so I think without

if it is without...then your pmf is not correct

what is it mean by "replacement"?

I think ,from the wording; we are pulling two balls out at the same time

that is what I am thinking

so you need to redo your pmf

if you get black balls then you get $2 each correct

yes

so one possibility is that you win $4

white ball, I lost $1

BB=$4
BO=$2
OB=$2
BW=$1
WB=$1
...

so X can take the values 4,2,1,0,-1,-2

agree?

oh, I see, I omitted orange which I shouldn't have

so how would I write PMF?

what i s the probability of 2 blacks? ie $4

(8/14)*(7/13)

ok
what about winning $2

(4/14)(2/13)
or
(2/14)(4/13)
?

winning $2 is BO or OB

there are 8 blacks...i see no 8's in your solution

lol.....there are 8 W

4 black...so prob of BB is
\[\frac{4}{14}\cdot\frac{3}{13}\]

not what you had above

so \[P(X=4)=\frac{4}{14}\cdot\frac{3}{13}\]

right , so for $2
(4/14)(2/13)
or
(2/14)(4/13)
(4/14)(2/13)+(2/14)(4/13)=

yes

the sum of the two

I understand now; I really appreciate your help

no problem