A box contains two coins: a regular coin and one fake two-headed coin (P(H) = 1). I

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A box contains two coins: a regular coin and one fake two-headed coin (P(H) = 1). I choose a coin at random and toss it twice. Define the following events.

  • A= First coin toss results in an H.
  • B= Second coin toss results in an H.
  • C= Coin 1 (regular) has been selected.

Find P(A|C),P(B|C),P(A ∩ B|C),P(A),P(B), and P(A ∩ B). Note that A and B are NOT independent, but they are conditionally independent given C.

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