Define the following two events for two tosses of a coin: A = at least one head

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Define the following two events for two tosses of a coin:
A = at least one head is obtained
B = both tails are obtained
a. Are A and B mutually exclusive events? Are they independent? Explain why or why not.
b. Are A and B complementary events? If yes, first calculate the probability of B and then calculate the probability of A using the complementary event rule.
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