On a game show there are five identical closed boxes. ONE box contains $10,000, TWO boxes contain $1,000 each, ONE box contains $1 and the remaining box contains a red card. A player is allowed to select a box, open it and keep the contents. The player is allowed to repeat this process until the box with the red card is opened; at this point the game ends. Find the probability of each possible outcome (so 0, 1, 1000, 1001, 2000, 2001, 10000, 10001,etc). As a check, remember that the sum of these probabilities should equal 1.
So for each X value and it corresponding P(X=x) I was trying to find them by saying all selection orders must end with a red card.
So I started by
X=0 --> P(x=X)= 1/5
X=1--> P(x=X)= 1C1*1C1/ 5C2 = 1/10
x=1000--> P(X=x)= 2C1*1C1/ 5C2= 2/10
x=1001--> P(X=x)= 2C1*1C1*1C1/ 5C3= 2/10
etc. but I do not get the probabilities to sum to one. (also trying this at X= 12,001 gives 1 which is obviously incorrect.) Is there a better way to go about this?
Any help would be greatly appreciated.
So for each X value and it corresponding P(X=x) I was trying to find them by saying all selection orders must end with a red card.
So I started by
X=0 --> P(x=X)= 1/5
X=1--> P(x=X)= 1C1*1C1/ 5C2 = 1/10
x=1000--> P(X=x)= 2C1*1C1/ 5C2= 2/10
x=1001--> P(X=x)= 2C1*1C1*1C1/ 5C3= 2/10
etc. but I do not get the probabilities to sum to one. (also trying this at X= 12,001 gives 1 which is obviously incorrect.) Is there a better way to go about this?
Any help would be greatly appreciated.