Alice throws a pair of dice without being seen by Bob and tells him that both numbers are at least four. 1. What is the probability that their sum is 9? 2. What is the probability that both numbers are the same? Hint: the sample space in this problem is set S containing all pairs (1, 1) (1, 2). . .(1, 6) (2, 1) (2, 2). . .(2, 6) (6, 1) (6, 2). . .(6, 6). .

1. Alice throws a pair of dice without being seen by Bob and tells him that both numbers are at
least four.
1. What is the probability that their sum is 9?
2. What is the probability that both numbers are the same?
Hint: the sample space in this problem is set S containing all pairs
(1, 1) (1, 2). . .(1, 6)
(2, 1) (2, 2). . .(2, 6)
(6, 1) (6, 2). . .(6, 6).