2019年12月26日 · QUESTION: I roll a single six-sided die repeatedly, recording the outcomes in a string of digits. I stop as soon as the string contains "$123456$". What is the expected length of the string? My an...

2025年1月26日 · Let $E_i$ be the event that the subsequence of length six starting with the $i^\text{th}$ die ($1\le i\le n$) is equal to $123456$. We then define $B_i$ to consist of the $11$ indices $j$ such that $|i-j|\le 5$ , so that $j\in B_i$ whenever subsequence $i$ and subsequence $j$ have a die in common.

2022年4月20日 · There are two ways we can look at this issue - either through a Bayesian or Frequentist approach. The Bayesian approach would be to keep rolling the dice a very large number of times (possibly millions) and then record what percentage landed on each number and assign these as the probabilities for each number.

2011年9月10日 · Actually the probability of tossing 123456 in any order is 6!=720 times the probability of the probability of tossing 123456 in that order. The first is \frac{6!}{6^6} the second is \frac{1}{6^6}.

2024年2月16日 · A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently. What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$

2023年5月4日 · Question: We roll a 6-sided die n times. What is the probability that all faces have appeared in order, in some six consecutive rolls (i.e., what is the probability that the subsequence 123456 appears among the n rolls)? I came up with the following formula: P(n) = 6 {n-6} * (n-5) / 6 n

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2024年9月1日 · Perform an experiment rolling a 19-sided die {123456,789,10,11,12,13,14,15,16,17,18,19} Q1= What is the sample space? _', 2, 317 56, , 4,/0, /75 2, 3, /Y, /_r/??/ /} /9 Q2=Find P(2438) =7= ' VA '3 19 Q3= Is the event of getting a {3} simple, non-simple, or a non-event? $ im//( ??

An unbiased die, with faces numbered $1,2,3,4,5,6$, is thrown $\mathrm{n}$ times and the list of $\mathrm{n}$ numbers showing up is noted. What is the probability that, among the numbers $1,2,3,4,5,6$, only three numbers appear in this list?

2024年1月30日 · We roll a 6-sided die n times. What is the probability that all faces have appeared in order, in some six consecutive rolls (i.e., what is the probability that the subsequence 123456 appears among the n rolls)? My immediate reflex was to use Markov chains, but I soon backed down because of how tedious the calculations seemed.