15 A four sided die has the numbers 1 2 3 4 printed on it th

15. A four sided die has the numbers {1, 2, 3, 4} printed on it; the die is a fair die.
A normal six

Solution

The sample space is

{(1,1), (1,2),   (1,3),   (1,4),   (1,5),   (1,6),
(2,1),   (2,2),   (2,3),   (2,4),   (2,5),   (2,6),
(3,1),   (3,2),   (3,3),   (3,4),   (3,5),   (3,6),
(4,1),   (4,2),   (4,3),   (4,4),   (4,5),   (4,6)}

Let Y be the product of the values from each die after both dice are tossed.

Thus Y take tha values 1,2,3,..., 24

Thus the sample space for Y is { Y : y=1,2, ...,24 }

The probability that Y=12 is

P(Y = 12) = P( (2,6), (3,4),(4,3))= 3/(24) = 1/8.