Well, there are a couple of things that you have to do here.

First, we must find the probability ofat least1 ball in a carton of 20 weighing less than 20g.

We can use a binomial distribution for this. Here's the formula.

X~binomial(k=20,p=0.02)

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 ity) 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~binomial(k=4, p=y)

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