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2 balls are chosen randomly from an urn containing 8 white, 4 black, 2 orange ball. Suppose you win 2 dollars for each black ball and lose 1 dollar for each white ball selected. Let X be the net winning , Find a) S_x my answer is for a) (-2,1,2)

Mathematics
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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

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Other answers:

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"?
if it is replacement then you pick a ball...look at it ..put it back then randomly sample again with all 14 balls
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

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