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Combination question - Average before same combination repeats


New member
Nov 29, 2013
Hi guys, hoping someone can help me with this. I’ve posted this on a couple other forums and so far I havent had any kind of solid answer on it! I was always better with words than numbers so I have no idea where to begin with this.

So imagine a combination lock with four values in length. The first value is from a choice of two numbers, the second from a choice of two numbers, the third from a choice of four numbers and the fourth from a choice of four numbers.

So it would look like this

?-?-?-? <-- possible combination made

If a combination was randomly generated, I’m trying to work out on average how many combinations you’d likely go through before one matched the first if 70% of the time the value in column A was the number 1 and 80% of the time the value in column B was the number 1 (the values in column C & D each have a 25% chance). So the odds percentage wise are;


I'm also interested in how to work that out so I can change values and percentages and come up with likely averages myself depending on what criteria I’m needing at the time.

Can anyone help and explain how it was worked out so I can learn for myself?