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Mathematics 340 - Fall 2015

Homework

  1. Suppose a coin is tossed three times.
    1. Find a sample space for this experiment.
    2. Find the event E that at least one toss is a head.
  2. Suppose a fuse is tested until it fails.
    1. Find a sample space for this experiment.
    2. Let $E_k$ be the event that a fuse fails in less than $k$ hours, $k = 1, 2, \ldots$. Find
      1. $E_1 \cup E_2 \cup E_3$
      2. $E_1 \cap E_2 \cap E_3$
      3. $E_3 \cap E_2^c$
      4. $\cup_{k=1}^\infty E_k$
      5. $\cap_{k=1}^\infty E_k$