## Libniz 3 years ago 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)

1. Libniz

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

2. Libniz

@zarkon

3. Libniz

@myininaya

4. MathLegend

What type of math is this? Algebra 1?

5. MathLegend

Honestly, I have no clue.

6. OpenstudyUser

lol

7. Libniz

probability

8. Zarkon

sampling with or without replacement?

9. Libniz

didn't say anything about replacement so I think without

10. Zarkon

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

11. Libniz

what is it mean by "replacement"?

12. Zarkon

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

13. Libniz

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

14. Zarkon

that is what I am thinking

15. Zarkon

so you need to redo your pmf

16. Zarkon

if you get black balls then you get $2 each correct 17. Libniz yes 18. Zarkon so one possibility is that you win$4

19. Libniz

white ball, I lost $1 20. Zarkon BB=$4 BO=$2 OB=$2 BW=$1 WB=$1 ...

21. Zarkon

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

22. Zarkon

agree?

23. Libniz

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

24. Libniz

so how would I write PMF?

25. Zarkon

what i s the probability of 2 blacks? ie $4 26. Libniz (8/14)*(7/13) 27. Zarkon ok what about winning$2

28. Libniz

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

29. Zarkon

winning $2 is BO or OB 30. Zarkon there are 8 blacks...i see no 8's in your solution 31. Zarkon lol.....there are 8 W 32. Zarkon 4 black...so prob of BB is $\frac{4}{14}\cdot\frac{3}{13}$ 33. Zarkon not what you had above 34. Zarkon so $P(X=4)=\frac{4}{14}\cdot\frac{3}{13}$ 35. Libniz right , so for$2 (4/14)(2/13) or (2/14)(4/13) (4/14)(2/13)+(2/14)(4/13)=

36. Zarkon

yes

37. Zarkon

the sum of the two

38. Libniz

I understand now; I really appreciate your help

39. Zarkon

no problem