Does anybody know why paying individually on a date is called "going Dutch"? Likewise, what is the etymology of the Dutch 200 game? These are interesting puzzles in and of themselves. I'm going to send EB down that path if he is interested in continuing his work on Holschuh's Etymological Dictionary of Bowling.
Anyway, today's challenge is about the Dutch 200 game. According to last year's USBC Rulebook, a Dutch 200 Game is "A game of alternating strikes and spares with a game total of 200." If you were fortunate enough to bowl one of these last year, you would have received a patch for it. However, the special achievement awards appear to have been eliminated from the most recent rulebook.
A game of alternating strikes and spares will always result in a score of 200 because 20 pins will be garnered for each frame, and it does not matter whether the first frame is a strike or a spare. This is a very rare occurrence in bowling, and today's puzzler concerns that rarity. Let's assume that we are dealing with a very skilled bowler. So, assume this:
1. The probability of getting a strike on a given frame is 50%.
2. If that bowler does not get a strike, the probability of picking up a spare is 75%.
For a single game bowled, what is the probability of this bowler getting a Dutch 200 game? Or put another way, how many games on average would have to be bowled for one of them to be a Dutch 200 game?
[Good luck. You're gonna need it!]
Click on the icon to the right for the answer.
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