Expected Value of carnival game: $.50 to play, $0.25 back if

[Angela123]

Assume that the pond contains 100 fish: 76 orange, 23 silver,
and 1 green. A contestant pays $0.50 to randomly catch one
fish and receives $0.25 if the fish is orange, $0.75
if the fish is silver, and $10.00 if the fish is green.

How much (on average) does the carnival gain on each play? (If the carnival
looses money, enter a negative dollar amount)

I tried doing this one by seeing what they would make if 100 people played but my answer didn't seem right. Is this problem easier than I am making it to be?

 

[Deleted member 4993]

Re: Expected Value

Assume that the pond contains 100 fish: 76 orange, 23 silver,
and 1 green. A contestant pays $0.50 to randomly catch one
fish and receives $0.25 if the fish is orange, $0.75
if the fish is silver, and $10.00 if the fish is green.

How much (on average) does the carnival gain on each play? (If the carnival
looses money, enter a negative dollar amount)

I tried doing this one by seeing what they would make if 100 people played but my answer didn't seem right. Is this problem easier than I am making it to be?

Could you please share your work with us - so that we know where to begin to help you.

Please also tell us - what is the definition of expected value.

 

[Angela123]

Re: Expected Value

(76*$.25)+(23*$.75)+(1*$10)=$46.25
(100 people *$.5)=$50
$50-$46.25=$3.75

Expected Value=E[x]=X1P1+X2P2+...+XkPk (also called the mean)

 

[Deleted member 4993]

Re: Expected Value

(76*$.25)+(23*$.75)+(1*$10)=$46.25
(100 people *$.5)=$50
$50-$46.25=$3.75 This is correct - however, remember that you have been asked to find the expected value per play.
Expected Value=E[x]=X1P1+X2P2+...+XkPk (also called the mean)

The definition of expected value is correct - however, it is not called mean. Mean is same as average - at the definition level it does not involve probabilities {P[sub:31j7bkg1]k[/sub:31j7bkg1]}

 

[Angela123]

Re: Expected Value

Oh I see, but how do I find the value per play? That's the part where I am stuck.

 

[Deleted member 4993]

Re: Expected Value

Oh I see, but how do I find the value per play? That's the part where I am stuck.

Really...

100 plays he is expected to make profit of ±X dollars

So his profit per play is ± X/100 dollars.