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
(I just need a diagram. I have no idea on how to draw the diagram so I need your help plzzzz! Just send me a pic of how you drew the diagram and that’s it!)
Answers
Answer:
Step-by-step explanation:
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 }
product of the two numbers is (i) A prime number 2 , 3 , 5 , 7
8 Possible Case
Probability = 8/64 = 1/8
(ii) Not a perfect square = 1 - perfect Square
Perfect Square 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64
possible Cases = 12
Probability = 1 - 12/64 = 1- 3/16 = 13/16
(iii) A multiple of 5 = 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 ,
15 possible Cases
Probability = 15/64
(iv) Less than or equal to 21
possible cases = 40
Probability = 40/64 = 5/8
(v) Divisible by 4 or 6 , 4 , 6 , 8 , 12 , 16 , 18 , 20 , 24 , 28 , 30 , 32 , 36 , 40 , 42 , 48 , 56 , 64
42 possible cases
Probability = 42/64 = 21/32
Learn more:
You are given one 6 sided dice and an 8 sided dice. The 8 sided die
six faces of a dice are numbered 1,2,2,3,3,6. The dice is rolled twice ...
Given : 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.
To find : Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
Solution:
Possible out put of 8-sided fair die
= { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }
Possible output if rolled twice
8 * 8 = 64
as u asked for Diagram only : its attached
Die Product
1,1 1
1,2 2
1,3 3
1,4 4
1,5 5
1,6 6
1,7 7
1,8 8
2,1 2
2,2 4
2,3 6
2,4 8
2,5 10
2,6 12
2,7 14
2,8 16
3,1 3
3,2 6
3,3 9
3,4 12
3,5 15
3,6 18
3,7 21
3,8 24
4,1 4
4,2 8
4,3 12
4,4 16
4,5 20
4,6 24
4,7 28
4,8 32
5,1 5
5,2 10
5,3 15
5,4 20
5,5 25
5,6 30
5,7 35
5,8 40
6,1 6
6,2 12
6,3 18
6,4 24
6,5 30
6,6 36
6,7 42
6,8 48
7,1 7
7,2 14
7,3 21
7,4 28
7,5 35
7,6 42
7,7 49
7,8 56
8,1 8
8,2 16
8,3 24
8,4 32
8,5 40
8,6 48
8,7 56
8,8 64
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