When coin 1 is flipped, it lands on heads with probability 3; when coin 2 is flipped it lands on heads with probability 10. (a) If coin 1 is flipped 12 times, find the probability that it lands on heads at least 10 times. (b) If one of the coins is randomly selected and flipped 10 times, what is the probability that it lands on heads exactly 7 times? (c) In part (b), given that the first of these 10 flips lands on heads, find the conditional probability that exactly 7 of the 10 flips land on heads.

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