A fair die is rolled. If an even number is obtained, then that is the recorded score. However, if an odd number is obtained, then a lair coin is tossed. If a head is obtained, then the recorded score is the number on the die, but if a tail is obtained, then the recorded score is twice the number on the die.
(a) Give the possible values of the recorded score.
(b) What is the probability that a score of 10 is recorded?
(c) What is the probability that a score of 3 is recorded?
(d) What is the probability that a score of 6 is recorded?
(e) What is the probability that a score of 4 is recorded if it is known that the coin is tossed? (f) If a score of 6 is recorded, what is the probability that an odd number was obtained on the die?