Suppose there are two coins, with coin landing heads when flipped with probability .3 and coin with

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Suppose there are two coins, with coin landing heads when flipped with probability .3 and coin with probability .5. Suppose also that we randomly select one of these coins and then continually flip it. Let Hj denote the event that flip j, j ≥ 1, lands heads. Also, let Ci be the event that coin i was chosen, i = 1, 2.

a. Find P(H1).

b. Find P(H2 | H1).

c. Find P(C1|H1).

d. Find P(H2H3H4|H1).

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