Good evening Skippy,

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 thatexactly0 successes occur. For the answer, the math, and all the sugar coated toppings, go here:

Binomial Distribution

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:

Binomial Distribution

n and p are the same from question a, but now, our k is 4. Press the 2nd button, "no morethan 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.

Any questions?