I have a big question to ask about probabilities and estimated value.
The problem is there are 4 cups. In each cup there is 4 jellybeans. One green,one red, one blue, one orange. You have to pick one jellybean out of each cup. If you get 2 of the same, you get 50 dollars. If you get 3, 100 dollars. If you get all 4, you get 150 dollars.
So can someone help me with finding the probabilities?

- anonymous

- katieb

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- Owlfred

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

- anonymous

Ok, so it doesn't matter which one you pick from the first cup, but for all other cups they have to match it.
So whichever one you pick in the first cup, what are the odds that you'll get the same from the second?

- anonymous

err the probability rather. odds is something different.

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## More answers

- anonymous

i was thinking since a cup has 4 jelly beans and 1 each of a color so to get like example red u have a 1/4 chance to get it out of a cup...but idk..lol if it makes sense?

- anonymous

So to calculate the amount of probabilities, I have to find the chances of getting 1 1 0 0 then 1010 then so on and so on?

- anonymous

No no no. You just have to find the probability for one cup. For example, if I pick a red bean first, what is the probability I'll get a red bean second?

- anonymous

but then i have to do it with each color :P so after wards calculating teh amount of getting 2s, i have to find 3s, 1110 1011 1101 and so on?

- anonymous

they are independent of each other the color of bean you get. The amount of money is not

- anonymous

Yes, but the probability will tell you what the expected earning is.

- anonymous

So start with the first case. No matter which color you pick from the first cup, what is the probability you will pick that same color in the second cup?

- anonymous

1/4 Chance to get it from the first cup, but to get from second cup would i use a P(A and B) formula?

- anonymous

Yes.

- anonymous

Well wait.

- anonymous

What do you mean by a 1/4 chance for the first cup?

- anonymous

The first cup doesn't matter. You can pick any color.

- anonymous

Oh.

- anonymous

You have a 1/4 chance for the second cup to match the first.

- anonymous

and a 1/4 chance for the 3rd cup.

- anonymous

and a 1/4 chance for the 4th cup.

- anonymous

So P(A and B and C)

- anonymous

so that means to get 4 straight of the same color its a 1/64 chance?

- anonymous

Right.

- anonymous

Mhm. so if i wanted to find three of the same color, it would be P(A and B) and to find two just P(A) ?

- anonymous

yep.

- anonymous

So in an estimated value write out...
1/4(50) + 1/16(100) + 1/64(150) ?Or must I do this for every color

- anonymous

Nope, that's it. It doesn't matter which color you get first.

- anonymous

:0 no way, wouldnt i have to do 1/4(50) + 1/4(50) + 1/4(50) + 1/4(50) to represent the 4 different colors i might get?

- anonymous

And the nrepeat with the others?

- anonymous

No. Because you'll only pick 1 of those 4 colors.

- anonymous

And whichever one you pick you'll only have a 1/4 chance to get the same color on your next pick.

- anonymous

It seems too simple to be true :0

- anonymous

The expected earning is how much you will make on average per attempt.

- anonymous

Each attempt you're only dealing with one color (the one you pick in the first cup).

- anonymous

Mathematics is often easier than you think.

- anonymous

Hmm, so if im trying to price this game like how much people have to pay to play

- anonymous

I just do the estimated value out

- anonymous

and just price on that number? So in this case its 21.1, so i might price it at 25?

- anonymous

And add your profit margin.

- anonymous

yeah.

- anonymous

Haha wow, in that case i think im good =D Thanks so much for your help! Ill post here if another problem arises :D

- anonymous

Will fan you! :D

- anonymous

be sure to click good answer to mark this question as solved.

- anonymous

Ohh mmkay no problem

- anonymous

Wait a minute, doesn't the probabilities have to add up to 1?

- anonymous

!!!

- anonymous

!

- anonymous

No they don't. The probability that you will pick a red, plus the probability to pick a green, plus the probability you will pick a blue, plus the probability you will pick an orange must add to one. But you don't care about those. You just want to know the probability you will pick the same color you picked from the first cup. If it added to 1 that would mean that you would always get the same color.

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