anonymous
  • anonymous
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?
Mathematics
katieb
  • katieb
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Owlfred
  • 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
  • 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
  • anonymous
err the probability rather. odds is something different.

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anonymous
  • 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
  • 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
  • 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
  • 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
  • anonymous
they are independent of each other the color of bean you get. The amount of money is not
anonymous
  • anonymous
Yes, but the probability will tell you what the expected earning is.
anonymous
  • 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
  • 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
  • anonymous
Yes.
anonymous
  • anonymous
Well wait.
anonymous
  • anonymous
What do you mean by a 1/4 chance for the first cup?
anonymous
  • anonymous
The first cup doesn't matter. You can pick any color.
anonymous
  • anonymous
Oh.
anonymous
  • anonymous
You have a 1/4 chance for the second cup to match the first.
anonymous
  • anonymous
and a 1/4 chance for the 3rd cup.
anonymous
  • anonymous
and a 1/4 chance for the 4th cup.
anonymous
  • anonymous
So P(A and B and C)
anonymous
  • anonymous
so that means to get 4 straight of the same color its a 1/64 chance?
anonymous
  • anonymous
Right.
anonymous
  • 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
  • anonymous
yep.
anonymous
  • 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
  • anonymous
Nope, that's it. It doesn't matter which color you get first.
anonymous
  • 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
  • anonymous
And the nrepeat with the others?
anonymous
  • anonymous
No. Because you'll only pick 1 of those 4 colors.
anonymous
  • anonymous
And whichever one you pick you'll only have a 1/4 chance to get the same color on your next pick.
anonymous
  • anonymous
It seems too simple to be true :0
anonymous
  • anonymous
The expected earning is how much you will make on average per attempt.
anonymous
  • anonymous
Each attempt you're only dealing with one color (the one you pick in the first cup).
anonymous
  • anonymous
Mathematics is often easier than you think.
anonymous
  • anonymous
Hmm, so if im trying to price this game like how much people have to pay to play
anonymous
  • anonymous
I just do the estimated value out
anonymous
  • anonymous
and just price on that number? So in this case its 21.1, so i might price it at 25?
anonymous
  • anonymous
And add your profit margin.
anonymous
  • anonymous
yeah.
anonymous
  • 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
  • anonymous
Will fan you! :D
anonymous
  • anonymous
be sure to click good answer to mark this question as solved.
anonymous
  • anonymous
Ohh mmkay no problem
anonymous
  • anonymous
Wait a minute, doesn't the probabilities have to add up to 1?
anonymous
  • anonymous
!!!
anonymous
  • 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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