A case of bad luck: Super Mario statistics

Playing through New Super Mario Bros. 2.  In world 3-A, you hit a rotating item block that cycles between a super mushroom, a 1-up mushroom, a fire flower, and a golden flower.  (You can see it at around the 3:02 mark in this video.)  When you hit the block, whichever item is currently in rotation pops out the top.  Assuming that you hit the block at a reasonably random time, you have a 25% chance of getting any particular item.

I wanted to get the golden flower in order to be able to remove the blocks and open up a pipe further on.  How many times did I have to try before I got the golden flower?  24.

What are the chances that, assuming each item appears randomly, it would take 24 tries to get the golden flower?  If my statistics are right, it’s along the lines of (3/4)^(24-1) (the chance that something that’s not the golden flower appears 23 times in a row), or about 0.13%.

Just a short story of my rotten luck of the day.  :-)

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