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Probability

Jan's big brown dog Shtutzy has recently learned how to open the fridge. One day Jan leaves a dozen (12) eggs in the fridge. Two of the eggs are rotten. the rest are good. When Jan comes home, the fridge is ransacked. Among other things, Shtutzy ate 5 eggs out of the dozen. Assume that she picked the eggs at random without any attention to whether the eggs are good or not. (Note: Binomial coefficients need NOT be evaluated in the followings.)
(a) What is the probability that Shtutzy ate the two rotten eggs?
(b) Shtutuzy is known to have a "stomach of steel". If she eats one rotten egg, she will be sick with probability 0.2. If she eats two rotten eggs, she will be sick with probability 0.5. If she does not eat any rotten egg. She will still be sick with probabilIty 0.01 from eating too much. What is the chance that Shtutzy will be sick?
(c) I have a good news: Shtutzy is not sick. Given this information, find the probahility that Shtutzy ate the two rotten eggs.

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A probabilty word problem is solved. The solution is detailed and well presented.

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