A fair dice has six faces numbered 1, 1, 1, 2, 3, & 4.
The dice is rolled twice and the number is shown recorded each time.
Find the probability that the sum of the two numbers recorded is at least 4.
+248 There are 6*6=36 possible rolls, and while some of these are the same they need to be counted multiple times because they have a higher chance of occuring.
Rolls that sum to 4, with frequency:
(1,3) x3
(3,1) x3
(2,2) x1
Sum to 5:
(1,4) x3
(4,1) x3
(3,2) x1
(2,3) x1
Sum to 6:
(3,3) x1
(2,4) x1
(4,2) x1
Sum to 7:
(3,4) x1
(4,3) x1
8:
(4,4) x1
Adding up the frequencies gets 21
The probability is 21/36=7/12
