I will explain my problems below
Get a number answer to each of the following. Note that in playing this lottery, the player has to select 5 numbers from the set of positive integers 1 to 49.
a) Find the probability of selecting none of the set of 5 secret integers already selected by a lottery machine from the set of positive integers 1 to 49. Of course, you win nothing in cases like this!
The desired probability is: 1086008/1906884 which is wrong
I tried to get the answer by doing C(44,5)/C(49,5). I was thinking if I could find the number of combinations that are wrong with a combination of 5 numbers but without the certain 5 numbers (which is 49-5=44 numbers to choose from), then I could just divide that by all the combinations of 5 with the certain 5 numbers(49 numbers to choose from). I found that this was wrong.
b) Find the probability of selecting at least one of the set of 5 secret integers already selected by a lottery machine from the set of positive integers 1 to 49.
This probability is:
I'm not exactly sure how to go about this one, but I am thinking along the lines of multiplying comparisons together since the at least means 1 or greater
As said in comments, you are correct for (a). You just haven't simplified the fraction. Simplified, the fraction is $$\frac{38786}{68103}.$$
For (b), this is a great use of complementary probability. Instead of finding the probability that there is at least $1$, find the probability that there are $0$ numbers picked. Then subtract from $1$.
You already have the probability of $0$ numbers picked in part (a). So subtract this from $1$ to get your answer.
Complementary probability is an ingenious way to solve problems like these. Whenever you see something along the lines of "probability that at least 1", always think complementary.