## anonymous one year ago An urn contains six red balls, five white balls, and four black balls. Four balls are drawn from the urn at random without replacement. For each red ball drawn, you win $10, and for each black ball drawn, you lose$15. Let X represent your net winnings. Compute E(X), your expected net winnings.

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1. anonymous

Hya

2. anonymous

hello

3. anonymous

I'm not good at this :P

4. anonymous

I'll give you a medal :D

5. anonymous

I need help not medal lol

6. anonymous

:P

7. misty1212

HI!!

8. misty1212

i cannot think of a snappy way to do this, this is going to take like forever

9. misty1212

first you have to think of all the possible outcomes when you pick 4 balls

10. misty1212

then you have to compute the amount of money you win or lose for each case then you have to find the probability of each possible outcome then you have to multiply and add !

11. anonymous

12. misty1212

if i had like two hours i could lets at least begin

13. anonymous

sure thing thanks

14. misty1212

one possibility is you get all red and therefore win $40 the probability you get all red is $\frac{\binom{6}{4}}{\binom{4}{15}}$ 15. misty1212 ok that is not quite right, the probabilty is $\frac{\binom{6}{4}}{\binom{15}{4}}$ 16. misty1212 that is $$\frac{1}{91}$$ http://www.wolframalpha.com/input/?i=%286+choose+4%29%2F%2815+choose+4%29 17. misty1212 then you could have 3 red, one white, win$30 that probability is $\frac{\binom{6}{3}\times \binom{5}{1}}{\binom{15}{4}}$

18. misty1212

this is really just a start there are lots of other possibilities i can't think of a quick way to do this though

19. anonymous

so if i get this right this is how it goes. P(1 red)=6C1×9C315C4 P(2 red)=6C2×9C215C4 P(3 red)=6C3×9C115C4 P(4 red)=6C415C4 P(1 red) = 0.369; P(2 red) = 0.396; P(3 red) = 0.132; P(4 red) = 0.011.

20. anonymous

the problem gets tough here on out i don't know what to do from here

21. anonymous

P(1 red)=6C1×9C3/15C4 P(2 red)=6C2×9C2/15C4 P(3 red)=6C3×9C1/15C4 P(4 red)=6C4/15C4 correct way

22. anonymous

@kropot need your help from this part

23. anonymous

i didn't understand anything from here on out \

24. kropot72

P(1 black) = 0.484; P(2 black) = 0.242; P(3 black) = 0.32; P(4 black) = 0.001 E(X) = 10(0.369 + 0.396 + 0.132 + 0.011) - 15(0.484 + 0.242 + 0.032 + 0.001)

25. kropot72

E(X) = a loss of $2.41. 26. anonymous @kropot72 but we need to find the net winnings not loss 27. kropot72 Expected net winnings = -$2.41.

28. kropot72

"Net winnings" means (expected gains) - (expected losses). In this case the expected losses outweigh the expected gains.

29. anonymous

give me medal?