Suppose that two dice are tossed. For each die, it is equally likely that 1, 2, 3, 4, 5, or 6 dots will turn up. Let S be the sum of the two dice.
a. What is the probability that S will be 5 or 7?
b. What is the probability that S will be some number other than 4 or 8?
c. Let E1 be the event that the first die shows a 3. Let E2 be the event that S is 6. Are E1 and E2 independent events?
d. Again, let E1 be the event that the first die shows a 3. Let E3 be the event that S is 7. Are E1 and E3 independent events?
e. Given that S is 7, what is the probability that the first die showed 4 dots?
f. Given that the first die shows a 3, what is the probability that S is an even number?