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Counting and probability ZIML Challenge Problems Areteem Winter Camp Notes
A number between 0 and 50 is chosen on a number line (so the number is not necessarily an integer). The probability that the number is within 2 units of a multiple of 10 can be expressed as the reduced fraction P/Q for positive integers P and Q. What is P+Q?
Do you have trouble understanding the question? Or have trouble about how to start? Or do you get an answer that doesn't make sense?
Anyway, this is geometrical probability, abut length. The total length of the whole sample space is $50$. The desired intervals consist of numbers within 2 units of a multiple of $10$, thus we want $(8,12)$, $(18, 22)$, etc. Remember though, $0$ and $50$ are also multiples of $10$ and the interval near them are $(0,2)$ and $(48,50)$. Now the probability is just the total length of these intervals divided by $50$.
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