Question

help please i dont understand and my teacher wont answer :(

Answer 1

Answer:

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

hope it helps..