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.
E(X) =

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.
E(X) =

anonymous · Answer

the amount you win times the probability you win it

anonymous · Answer

oh actually i see that this will take some work
ready?

anonymous · Answer

yes I am

anonymous · Answer

first you need the probability for every event in the sample space
there are 5 of them, because you could pick 
0 red 4 black
1 red 3 black
2 red 2 black
3 red 1 black
4 red 0 black

anonymous · Answer

okay

anonymous · Answer

we can compute the probability of each of these, and also we need to compute how much money you make for each outcome

anonymous · Answer

when i say "can" i mean "must"

anonymous · Answer

okay, is it not just asking for the winnings... why do I need the probability?

anonymous · Answer

the second part should be easy
0  red 4 black, lose $4\times 15=\$60$ so $-60$ for that one

anonymous · Answer

do you know what the question is asking?

anonymous · Answer

net winnings

anonymous · Answer

no

anonymous · Answer

expected winning, not "net winnings"

anonymous · Answer

okay

anonymous · Answer

expected value i like an average
what would you expect to win, on average, for one play of the game

anonymous · Answer

1

anonymous · Answer

?

anonymous · Answer

nm

anonymous · Answer

to compute that average, you need to know the probability you win each of the possible amounts you can win 
now that we know there are 5 possible outcomes, which i listed above, you have to find first how much money you win (or lose) for each of those outcomes

anonymous · Answer

okay

anonymous · Answer

so for red it is $60

anonymous · Answer

what does "for red it is 60" mean?

anonymous · Answer

from your earlier post

anonymous · Answer

do you see above i listed all 5 possible outcomes?

anonymous · Answer

yes I see that and I understand that the we need to do it for the remaining ones as well

anonymous · Answer

right
none of those outcomes was "red"

0 red, 4 black, $\to -60$ the minus sign because you lost

anonymous · Answer

oh okay

anonymous · Answer

1 red, 3 black $10-45=-35$ so 
1 red, 3 black $\to -35$

anonymous · Answer

you can do the rest, i will be right back, let me know what you get
then we have to compute the probability of each one, i will help with that