Probability Help: Find Probability of Uncracked Egg Carton

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The probability of a carton of eggs having at least one cracked egg is 0.04. To find the probability that the carton is fine, or contains no cracked eggs, one can use the principle that the sum of all possible outcomes equals 1. Therefore, the probability of having no cracked eggs is 1 - 0.04, which equals 0.96. This understanding simplifies the problem significantly, demonstrating that the solution is straightforward once the concept is grasped. The discussion emphasizes the importance of recognizing complementary probabilities in solving such problems.
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Homework Statement



The question states: The probablity that a carton of eggs has a (at least one) cracked egg is .04. What is the probability that your carton is fine?


Homework Equations





The Attempt at a Solution



I'm not sure how to go about this one. I'm pretty comfortable with the beginning probability stuff, but I'm sure as to which equation applies here. If someone can point me in the right direction I would be so grateful.

Thank you very much.
 
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What is the sum of the probabilities that i) the carton contains at least one cracked egg and ii) the carton contains no cracked eggs?
 
Think about it, if the probability of having AT LEAST 1 is 0.04, what is the probability of having NONE?

For another question with a similar answer that may help you understand what the question is asking:

If the probability of winning a draw is 5%(no ties are possible), what is the probability that you will lose? Well what are the possibilities... You could either win or lose. So if you have a 5% chance of winning, you must have a 95% chance of losing.

edit: As Dick said, the sum of all the possible outcomes is always 1.00 (100%). So p(at least 1) + p(0) = 1, right?
 
Last edited:
That completely makes sense now. I feel kind of stupid now cause it's actually super easy.

Thank you for helping.
 

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