Well, there are a couple of things that you have to do here.
First, we must find the probability of at least 1 ball in a carton of 20 weighing less than 20g.
We can use a binomial distribution for this. Here's the formula.
X= the number of balls that weigh less than 20g.
We're looking for
Using the Axioms of Probability this can be rewritten as which is the same as
Using the binomial distribution formula given above solve
Your answer (I'll call it y) will be used in the second part.
Now we need to find the probability that out of 4 randomly selected cartons, exactly 2 will have at least 1 ball that does not meet the minimum weight requirement.
Again, we can use a binomial distribution.
X= the number of cartons that have at least 1 ball that does not meet the minimum weight requirement.
Now simply use the binomial distribution formula to solve