Question

A pyramid-shaped 4-sided die with sides 1, 2, 3, 4 is rolled along with a cube-shaped 6-sided die

with sides 1, 2, 3, 4, 5, 6.

What is the Sample Space? What are the probabilities of each element in the Sample Space? State the probabilities of all possible sums of the 2 rolled numbers (events).

Answer 1

4 sided die with sides 1,2,3,4 have outcomes 1,2,3,4

6 sided die has outcomes 1,2,3,4,5,6

Sample space for two die rolling is

sample space = { ( 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 )}

So there are 4*6 = 24 outcomes.

probability of each outcome is = 1/24 = 0.0.0417

sample space	Probability	sum
( 1 , 1 )	=1/24=0.0417	2
( 1 , 2 )	0.0417	3
( 1 , 3 )	0.0417	4
( 1 , 4 )	0.0417	5
( 1 , 5 )	0.0417	6
( 1 , 6 )	0.0417	7
( 2 , 1 )	0.0417	3
( 2 , 2 )	0.0417	4
( 2 , 3 )	0.0417	5
( 2 , 4 )	0.0417	6
( 2 , 5 )	0.0417	7
( 2 , 6 )	0.0417	8
( 3 , 1 )	0.0417	4
( 3 , 2 )	0.0417	5
( 3 , 3 )	0.0417	6
( 3 , 4 )	0.0417	7
( 3 , 5 )	0.0417	8
( 3 , 6 )	0.0417	9
( 4 , 1 )	0.0417	5
( 4 , 2 )	0.0417	6
( 4 , 3 )	0.0417	7
( 4 , 4 )	0.0417	8
( 4 , 5 )	0.0417	9
( 4 , 6 )	0.0417	10

Probability that all possible sums of two rolls
sum (Y)		Probability P(y)
2		0.0417
3		0.0834
4		0.1251
5		0.1668
6		0.1668
7		0.1668
8		0.1251
9		0.0834
10		0.0417