The formula for binomial probabilities is-

According to the problem, n = 12, p = 0.42. Since the selection is 12 adults and the percentage is 42%.
Let's find q

For (a) exactly three, x = 3. So, let's replace all the values in the formula.

Using a calculator, we have

This means the probability of exactly three is 12.1%, approximately.
For (b) at least four, we have to find probability when x = 4, 5, 6, 7, 8, 9, 10, 11, 12. Using a calculator, we find each probability, then we sum.


Now, we sum all.

Therefore, the probability of at least four is 81.5%, approximately.
At last, for (a) at most two, the probability would be the sum of probabilities when x = 1, 2.

So, the sum would be

Therefore, the probability of at most two is 6.3%, approximately.