Question

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

Answer 1

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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