A Christmas fruitcake has Poisson-distributed independent numbers of sultana raisins, iridescent red cherry bits, and radioactive green cherry bits with respective averages 48, 24, and 12 bits per cake. Suppose you politely accept 1/12 of a slice of the cake. (a) What is the probability that you get lucky and get no green bits in your slice? (b) What is the probability that you get really lucky and get no green bits and two or fewer red bits in your slice? (c) What is the probability that you get extremely lucky and get no green or red bits and more than five raisins in your slice?
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