Dungeons and Dragons: Part A A 20-sided die is often used in tabletop role-playing games like Dungeons and Dragons.  During the game players may face something called a "skill check" where they must roll a 20-sided die and get a result equal to or above a given value.  For example, a player may be required to roll a 15 or above in order to succeed and pass the skill check.  Rolling a 14 or lower would be a failure.   If the player rolls the die 10 times in a row, what is the expected number of rolls that would pass the skill check by rolling as a 15 or higher?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Dungeons and Dragons: Part A

20-sided die is often used in tabletop role-playing games like Dungeons and Dragons.  During the game players may face something called a "skill check" where they must roll a 20-sided die and get a result equal to or above a given value.  For example, a player may be required to roll a 15 or above in order to succeed and pass the skill check.  Rolling a 14 or lower would be a failure.  

If the player rolls the die 10 times in a row, what is the expected number of rolls that would pass the skill check by rolling as a 15 or higher?

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