TITLE: On average, how many times will I need to roll a six-sided die before I see ten ONES in total?
QUESTION [5 upvotes]: On average, how many times will I need to roll a six-sided die before I see ten ONES in total?
I'd like to be able to extend my knowledge to answer other questions in the same form, such as, "If only 15% of fish are within the legal size limit, how many fish should I need to catch before I get five keepers?
Thanks kindly

REPLY [2 votes]: Expected value is additive, so the expected number of times you need to roll the die to see 10 ones is 10 times the expected value of times you must roll the die to get a one. If after performing an experiment the probability of an event is $p$, the expected value of repetitions of the experiment needed for the event to occur is the inverse of the probability $1/p$. The probability of getting a one after rolling a die is $1/6$, so the expected number of times you need to roll a die to see a one is 6. Because of the additive property mentioned above, the expected number of times you need to roll the die to get 10 ones is $10 \times 6 = 60$.