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)

Question

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)

anonymous · Answer

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

anonymous · Answer

@zarkon

anonymous · Answer

@myininaya

mathlegend · Answer

What type of math is this? Algebra 1?

mathlegend · Answer

Honestly, I have no clue.

openstudyuser · Answer

lol

anonymous · Answer

probability

zarkon · Answer

sampling with or without replacement?

anonymous · Answer

didn't say anything about replacement so I think without

zarkon · Answer

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

anonymous · Answer

what is it mean by "replacement"?

zarkon · Answer

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

anonymous · Answer

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

zarkon · Answer

that is what I am thinking

zarkon · Answer

so you need to redo your pmf

zarkon · Answer

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

anonymous · Answer

yes

zarkon · Answer

so one possibility is that you win $4

anonymous · Answer

white ball, I lost $1

zarkon · Answer

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

zarkon · Answer

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

zarkon · Answer

agree?

anonymous · Answer

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

anonymous · Answer

so how would I write PMF?

zarkon · Answer

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

anonymous · Answer

(8/14)*(7/13)

zarkon · Answer

ok


what about winning $2

anonymous · Answer

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

zarkon · Answer

winning $2 is BO or OB

zarkon · Answer

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

zarkon · Answer

lol.....there are 8 W

zarkon · Answer

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

zarkon · Answer

not what you had above

zarkon · Answer

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

anonymous · Answer

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

zarkon · Answer

yes

zarkon · Answer

the sum of the two

anonymous · Answer

I understand now; I really appreciate your help

zarkon · Answer

no problem