If a dozen of eggs has one bad egg it will be replaced.Probability that an egg is bad is 0.05. What is the probability that dozen will have to be replaced

Question

I know this question relates to the binomial distribution is a sampling  distribution but I am still having trouble with it.

Answer 1

Sometimes it's easier to calculate the probability that something will not happen than the probability that it will happen.  Since these 2 events are mutually exclusive and span the entire probability space their probabilities must sum to 1, so P(have to be replaced) = 1 - P(not have to be replaced).  So see if you can figure out P(not have to be replaced).  

 

Hint:  Since P(bad egg) = 0.05, what is P(good egg)?  

         What is P(all 12 eggs in a dozen good)?  

 

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