State true or false.Two dice are numbered

1,2,3,4,5,6
, and

1,1,2,2,3,3
, respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting each sum from

2
to

9
separately will all be equal to

1
6

.

Question

State true or false.Two dice are numbered

1,2,3,4,5,6
 , and

1,1,2,2,3,3
 , respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting each sum from

2
  to

9
  separately will all be equal to

1
    6

.

Accepted Answer

It is given that, two dice are numbered

1,2,3,4,5,6
  and

1,1,2,2,3,3
 .We have to find the probability of getting each sum from

2
  to

9
  separately.The total number of possible outcome for two dice is

36
 .The favorable outcome for sum of the number on

2
  dice is

2
  are

(1,1)
  and (1,1).The probability for the sum of the number on both dice is

2
  is,

P(sum is 2)=
    2
    
     36

=
    1
    
     18

The favorable outcome for sum of the number on two dice is 3 are

(1,2),(1,2),(2,1),(2,1)
 . The number of favorable outcome is

4
 . The probability for the sum of the number on both dice is

3
  is,

P(sum is 3)=
    4
    
     36

=
    1
    9

The favorable outcome for sum of the number on two dice is

4
  are

(2,2),(2,2),(3,1),(3,1),(1,3),(1,3)
 . The number of favorable outcome is

6
 . The probability for the sum of the number on both dice is

4
  is,

P(sum is 4)=
    6
    
     36

=
    1
    6

The favorable outcome for sum of the number on two dice is

5
  are

(2,3),(2,3),(3,2),(3,2),(4,1),(4,1)
 .The number of favorable outcome is

6
 . The probability for the sum of the number on both dice is

5
  is,

P(sum is 5)=
    6
    
     36

=
    1
    6

The favorable outcome for sum of the number on two dice is

6
  are

(4,2),(4,2),(3,3),(3,3),(5,1),(5,1)
 . The number of favorable outcome is

6
 . The probability for the sum of the number on both dice is

6
  is,

P(sum is 6)=
    6
    
     36

=
    1
    6

The favorable outcome for sum of the number on two dice is

7
  are

(5,2),(5,2),(6,1),(6,1),(4,3),(4,3)
 . The number of favorable outcome is

6
 . The probability for the sum of the number on both dice is

7
  is,

P(sum is 7)=
    6
    
     36

=
    1
    6

The favorable outcome for sum of the number on two dice is

8
  are

(6,2),(6,2),(5,3),(5,3)
 . The number of favorable outcomes is 4 . The probability for the sum of the number on both dice is

8
  is,

P(sum is 8)=
    4
    
     36

=
    1
    9

The favorable outcome for sum of the number on two dice is

9
  are

(6,3),(6,3)
 . The number of favorable outcome is

2
 . The probability for the sum of the number on both dice is 9 is,

P(sum is 9)=
    2
    
     36

=
    1
    
     18

Hence the probabilities are:

P(sum is 2)=
      1
      
       18
     
     ,P(sum is 2)=
      1
      
       18
     
     ,P(sum is 3)=
      1
      9
     
     ,P(sum is 4)=
      1
      6
     
     ,P(sum is 5)=
      1
      6
     
     ,

P(sum is 6)=
      1
      6
     
     ,P(sum is 7)=
      1
      6
     
     ,P(sum is 8)=
      1
      9
     
     ,P(sum is 9)=
      1
      
       18

All the probabilities from

2
  to

9
  are not same as

1
    6

, they are different.Hence, the correct statement is the probability of getting each sum from 2  to 9 separately will all be equal to 16.Hence, the statement is false.Therefore, option 2 is correct.

State true or false.

Two dice are numbered $1, 2, 3, 4, 5, 6$ , and $1, 1, 2, 2, 3, 3$ , respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting each sum from $2$ to $9$ separately will all be equal to $16$ .

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State true or false.Two dice are numbered 1,2,3,4,5,6 , and 1,1,2,2,3,3 , respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting each sum from 2 to 9 separately will all be equal to 1 6 .

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State true or false.

Two dice are numbered $1, 2, 3, 4, 5, 6$ , and $1, 1, 2, 2, 3, 3$ , respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting each sum from $2$ to $9$ separately will all be equal to $16$ .