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I need help in settling a debate. If say I have a 1/5 chance of gaining promotion in a year, do the odds of gaining promotion increase as time progresses (all else being equal)?

Phrased negatively I can handle it i.e. chances of not gaining promotion after five years is 4/5^5 = 32%, 6years = 26% so it would seem yes that the odds increase (from a year 0 perspective)

But I get confused when I think of the chances of gaining promotion. Year 1 is 1/5 but how do I calculate all potential outcomes for year 2? It is still 1/5 for the 4 out of 5 times promotion isn't achieved in year 1 but how do I factor in that 1/5 chance it is got in year 1? Is it 4/20 in year 2 i.e. disregard the 1/5 from year 1 OR 9/25 i.e. If I get promotion in year 1 I will still have it in year 2 plus 1/5 * 4/5?

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# Idiot needs help

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