Q4. An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated. (a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
Answers
Given : 8-sided fair die is rolled twice and the product of the two numbers obtained
To find : possibility of the product of the two numbers appearing on the die in each throw
Solution:
8-sided fair Dice has output = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }
Dice is thrown twice so possible outputs are 8 * 8 = 64
= { (1 , 1) , ( 1 , 2) , ( 1, 3) , ( 1, 4 ) , ( 1, 5) , ( 1 , 6 ) , ( 1, 7 ) , ( 1, 8) ,
(2 , 1) , (2 , 2) , ( 2, 3) , ( 2, 4 ) , ( 2, 5) , (2 , 6 ) , ( 2, 7 ) , ( 2, 8) ,
(3 , 1) , ( 3, 2) , ( 3, 3) , ( 3, 4 ) , ( 3, 5) , ( 3 , 6 ) , (3, 7 ) , ( 3, 8) ,
(4, 1) , ( 4 , 2) , ( 4, 3) , ( 4, 4 ) , ( 4, 5) , (4 , 6 ) , (4, 7 ) , (4, 8) ,
(5, 1) , ( 5 , 2) , ( 5, 3) , (5, 4 ) , ( 5 ,5) , (5, 6 ) , ( 5, 7 ) , ( 5, 8) ,
(6 , 1) , ( 6 , 2) , ( 6, 3) , (6, 4 ) , ( 6, 5) , (6 , 6 ) , ( 6, 7 ) , ( 6, 8) ,
(7 , 1) , ( 7 , 2) , ( 7, 3) , ( 7, 4 ) , ( 7 , 5) , ( 7, 6 ) , ( 7, 7 ) , (7, 8) ,
(8 , 1) , ( 8 , 2) , (8, 3) , ( 8, 4 ) , ( 8, 5) , ( 8 , 6 ) , ( 8, 7 ) , ( 8, 8) }
Products
1 = ( 1, 1)
2 = ( 1, 2) , ( 2, 1)
3 = ( 1 , 3) , ( 3 , 1)
4 = (1 , 4) , ( 2, 2) , ( 4, 1)
5 = ( 1, 5) , ( 5 , 1)
6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)
7 = ( 1, 7) , ( 7 , 1)
8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)
9 = ( 3, 3)
10 = ( 2, 5) , ( 5, 2)
12 = (2 , 6) , ( 3 , 4) , ( 4 3) , ( 6 , 2)
14 = ( 2, 7) , ( 7 , 2)
15 = (3 , 5) , ( 5 , 3)
16 = (2 , 8) , ( 4 , 4) , ( 8 , 2)
18 = ( 3, 6) , ( 6 , 3)
20 = ( 4, 5) , ( 5, 4)
21 = ( 3 , 7) , ( 7 , 3)
24 = ( 3 , 8) , ( 4 , 6 ) , ( 6 , 4) , ( 8 , 3)
25 = ( 5 , 5)
28 = ( 4 , 7) , ( 7 , 4)
30 = ( 5 , 6) , ( 6 ,5 )
32 = ( 4 , 8) , ( 8 , 4)
35 = ( 5 , 7) , ( 7 , 5)
36 = (6 , 6)
40 = ( 5 , 8) , ( 8 , 5)
42 = ( 6 , 7) , ( 7 , 6)
48 = ( 6 , 8) , ( 8 , 6)
49 = ( 7 , 7)
56 = ( 7 , 8) , ( 8 , 8)
64 = ( 8 , 8)
Products = { 1 ,2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ,12 , 14 , 15 , 16 , 18 , 20 ,21 , 24 , 25 , 28 , 30 ,32 , 35 , 36 , 40 , 42 , 48 , 49 , 56 , 64 }
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