A housewife buys a dozen eggs out of which two turn out to be rotten. She chooses four eggs to scramble for breakfast. Find the chance that she chooses:

a) all good eggs

b)three good and one bad egg

c)two good and two bad eggs

d)atleast one bad egg

PLEASE HELP! :O

Total eggs = 12No of rotten eggs =2No of good eggs = 10Selecting any 4 eggs , S(E) = 12C4 = 12!/(8! 4!)  =495a) Probability of all good eggs= 10C4/S(E) = 210/495 = 14/33b)Probability of 3 good and 1 bad eggs = 10C3 ×  2C1/S(E) =120×2/495 = 16/33c)Probability of 2 good and 2 bad eggs = 10C2 ×  2C2/S(E) = 45×1/495 = 1/11d)Probability of atleast 1 bad egg= Probability of 1 bad egg + Probability of 2 bad eggs                                                    =16/33 + 1/11 = (16+3)/33 = 19/33

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