Greetings all!
First of, it's been a very long time since I took any sort of math class, and probability/statistics/combinatorics were subjects that I was never particularly good at, so any and all help is very much appreciated.
I'm looking to determine the average number of times it would take to "spin a wheel" that contained 10 different prizes, where each prize can only be obtained once, and the goal is obtain each prize. After a prize is collected, that 1/10th wedge of the wheel yields no prize, and you must spin again.
So far, all I've determined is that the probability is dependent, but I do not know how to proceed to come up with an answer (preferably with 95 or 99% certainty) as to how many spins it would take to collect each prize. (Again, each spin that lands on a previously claimed prize yields no prize, and would just add to the count of spins.)
On the first spin, the odds are 10/10 = 1 that you will land on an unclaimed prize.
Spin 1 - P(A): 10/10
P(B): 9/10
However, Spin 3 is not 8/10, as there is 1/10 chance that Spin 2 resulted in the same prize-slot as Spin 2.
If I want to count the probability that each spin lands on a new, unclaimed prize, then that would be:
P(A) = 10/10
P(B) = 9/10
P(C) = 8/10
...
P(J) = 1/10
P(A*B*C*...*J) = 0.00036288
I'm not sure how useful, if at all, the above solution is to solving this problem.
I've looked online reading numerous "probability basics" and I'm still not sure where to begin.
First of, it's been a very long time since I took any sort of math class, and probability/statistics/combinatorics were subjects that I was never particularly good at, so any and all help is very much appreciated.
I'm looking to determine the average number of times it would take to "spin a wheel" that contained 10 different prizes, where each prize can only be obtained once, and the goal is obtain each prize. After a prize is collected, that 1/10th wedge of the wheel yields no prize, and you must spin again.
So far, all I've determined is that the probability is dependent, but I do not know how to proceed to come up with an answer (preferably with 95 or 99% certainty) as to how many spins it would take to collect each prize. (Again, each spin that lands on a previously claimed prize yields no prize, and would just add to the count of spins.)
On the first spin, the odds are 10/10 = 1 that you will land on an unclaimed prize.
Spin 1 - P(A): 10/10
P(B): 9/10
However, Spin 3 is not 8/10, as there is 1/10 chance that Spin 2 resulted in the same prize-slot as Spin 2.
If I want to count the probability that each spin lands on a new, unclaimed prize, then that would be:
P(A) = 10/10
P(B) = 9/10
P(C) = 8/10
...
P(J) = 1/10
P(A*B*C*...*J) = 0.00036288
I'm not sure how useful, if at all, the above solution is to solving this problem.
I've looked online reading numerous "probability basics" and I'm still not sure where to begin.