Can someone check the following for me please? I'm confused by the wording of the question .

Consider the experiment of drawing 3 tickets without replacement from a box of tickets labeled {1, 2, 3, ... , 10}.

Let A be the event that at least one of the tickets drawn is labeled with an even number,

Let B be the event that at least one of the tickets drawn is labeled with a prime number,

Let C be the event that at least one of the tickets drawn is labeled with a number larger than 9, and

Let D be the event that the sum of the numbers on the tickets drawn is at least 25.

2. Are A and B mutually exclusive?

No (this would work since drawing a 2 would satisfies the even and prime factor)

3. Are A and Bc mutually exclusive?

No (unsure)

4. Are C and Dc mutually exclusive?

No (unsure)

What does Bc and Dc stand for here? So basically Bc would mean Not B... would it be fair to say that Bc = A∪C∪D?... so Dc = A∪B∪C

5. Which of the following is/are true (select all that apply)?

A. A implies B (even doesn't have to be prime)

B. B implies A (prime doesn't have to be even)

C. C implies D (having a 10 doesn't imply that the total sum will be 25; it could just be 10, 1, 2)

D. D implies C ***

E. none of the above

>>> D implies C since the sum total of 25 requires at least 10 to be in one of the selection. (10 + 9 + 6 or 10 + 8 + 7 are the only 2 solutions)... 9 + 8 + 7 is only 24, thus forcing D to include 10, thus satisfying C.

Thanks!