Could I get my work checked please

1.(5 pts.) Roll a fair, six - sided die once. Assume each side of the die is equally likely to appear face up when rolled.Let event A be the event an even number is face up when rolled.Let event B be the event of rolling more than a four.

a)(1 pt.) What is the sample space?

Event A- even number is face up

Event B- rolling more than a 4

1, 2, 3, 4, 5, 6

b)Are A and B mutually exclusive? Explain your reasoning.

No, because the events can happen at the same time; like rolling a 6 is even and more than 4.

c)Are A and B independent? Explain your reasoning.

P(A and B) = P(A) * P(B)