title: Simulation on the probability of doing laundry together
body: <p>I am trying to simulate a self-made probability problem &quot;Suppose there are 6 households living in a unit of an apartment complex. On average, a single household does laundry twice a week for 2 hours each time. Find the probability that any two households doing laundry at the same time.&quot;</p>
  <p>However, I was able to simulate for the case when a single household does laundry ONCE a week (R code below) and would appreciate any help on extending the code to the scenario for doing laundry TWICE a week.</p>
  <p>I also attempted to find a theoretical solution but it did not match with my simulation results below. Any help is appreciated. Thanks!</p>
  <pre><code>dist.min &lt;- function(x) {
      ifelse(min(dist(x)) &lt;= 2 * 3600 - 1, T, F)
  }
  
  set.seed(12345)
  N &lt;- 100000
  mat &lt;- matrix(sample(1:(24 * 60 * 60 * 7), N * 6, replace = T), ncol = 6)
  is.same &lt;- apply(mat, 1, dist.min)
  mean(is.same) # 0.30602
  </code></pre>