Question

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.

Answer 1

Hya

Answer 2

hello

Answer 3

I'm not good at this :P

Answer 4

I'll give you a medal :D

Answer 5

I need help not medal lol

Answer 6

:P

Answer 7

HI!!

Answer 8

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

Answer 9

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

Answer 10

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 !

Answer 11

could you lead me through the problem step by step please.

Answer 12

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

Answer 13

sure thing thanks

Answer 14

one possibility is you get all red and therefore win $40
the probability you get all red is \[\frac{\binom{6}{4}}{\binom{4}{15}}\]

Answer 15

ok that is not quite right, the probabilty is \[\frac{\binom{6}{4}}{\binom{15}{4}}\]

Answer 16

that is \(\frac{1}{91}\)
http://www.wolframalpha.com/input/?i=%286+choose+4%29%2F%2815+choose+4%29

Answer 17

then you could have 3 red, one white, win $30
that probability is
\[\frac{\binom{6}{3}\times \binom{5}{1}}{\binom{15}{4}}\]

Answer 18

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

Answer 19

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.

Answer 20

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

Answer 21

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

Answer 22

@kropot need your help from this part

Answer 23

i didn't understand anything from here on out \

Answer 24

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)

Answer 25

E(X) = a loss of $2.41.

Answer 26

@kropot72 but we need to find the net winnings not loss

Answer 27

Expected net winnings = -$2.41.

Answer 28

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

Answer 29

give me medal?