1. A red die and a green die are rolled as a pair. Let E be the event that "the red die shows a 2" and let F be the event that "the sum of the numbers is 8." Are the events E and F independent?
2. Suppose that we toss a coin three times and observe the sequence of heads and tails. Let E be the event that "the first toss lands heads" and F the event that "there are more heads than tails." Are E and F independent?
3. An urn contains four red balls labeled 1, 2, 3, and 4 and six green balls labeled 5, 6, 7, 8, 9, and 10. A ball is selected at random from the urn. Are the events "the ball is red" and "the number on the ball is even" independent events?
4. Two cards are drawn in succession (without replacement) from a deck of cards. Are the events "the first card is a king" and "the second card is red" independent events?
5. Two archers shoot at a moving target. One can hit the target with probability 1/4 and the other with probability 1/3. Assuming that their efforts are independent events, what is the probability that
(a) both will hit the target?
(b) at least one will hit the target?