perplexus.info :: Probability : Scratch a Home Run!

Scratch a Home Run! (Posted on 2005-10-18)

A scratch game has 16 covered squares, below which are, in some order, symbols representing 9 players (a pitcher, a catcher, and so on), 3 strikes (strike 1, strike 2, and strike 3), 1 hit, 1 home run, 1 bat, and 1 ball.

You start scratching squares randomly, and if you manage to get the hit and the home run you win (never mind other symbols) unless you already got the three strikes, because then you're out!

What are the odds of winning at this game?

Computer solutions welcome!

Submitted by e.g.

Rating: 2.0000 (3 votes)

Solution: (Hide)

The only things that matter are the three strikes, the hit, and the home run. You win if you get a permutation that ends with a strike, and lose otherwise. There are 20 different permutations (counting all strikes as equal) and 12 end with a strike, so your odds are 12/20=60%.
Even easier: 60% of the symbols are strikes, so those are the odds of your winning.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2022-09-02 22:36:24
Independent solution	Tristan	2005-10-18 20:03:51
re: By Computer?	derek	2005-10-18 10:45:49
My solution	Jer	2005-10-18 10:44:23
re: I agree with derek	derek	2005-10-18 10:42:23
I agree with derek	Steve Herman	2005-10-18 10:25:47
By Computer?	Old Original Oskar!	2005-10-18 09:33:39
By Computer?	Old Original Oskar!	2005-10-18 09:33:35
solution	derek	2005-10-18 09:19:52

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