Think of it this way, you have 2 events, success being a student who passes STAT111 also takes the course MATH108. This is p which is the probability of success.
You also have q, which is 1 - p, which is failure. That is 0.65, and that represents a student who passes STAT111 that does not take MATH108. That sounds like a binomial distribution. Since n = 10 which is small, we can skip doing the Poisson approximation to the binomial distribution.
For question A, you want the probability that exactly 0 successes occur. For the answer, the math, and all the sugar coated toppings, go here:
We already determined n is 10, p is 0.35, and for k, we want exactly k successess, k being 0. So, enter those 3 items, press the first button "exactly k successes" and check out the answer and the math.
I get 0.0135 rounding to 4 digits. Does that make sense?
Now for question b.
This time, they ask for "Less than half of the group of 10 students". n and p are still the same, nothing has changed there. 1/2 of 10 is 5. But they say "less than", not "less than or equal to" or "no more than". Less than 5 in integer terms means <= 4. We want P(x <= 4).
Go back to the same link:
n and p are the same from question a, but now, our k is 4. Press the 2nd button, "no more than k successes". I get 0.7516. Scroll down slowly and you will see each probability calculated for x = 0,1,2,3,4. Then check out the cumulative probability section towards the bottom. Notice that our probability for x = 0 matches our answer in question a.