State true or false.Two dice are rolled simultaneously. Consider the following table: A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

=
1

11

.

Question

State true or false.Two dice are rolled simultaneously. Consider the following table: A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

=
    1
    
     11

.

Accepted Answer

It is given a data,The probability of an event E is given as-

P(E)=
    
     Number of outcomes favourable to E
    
     Number of all possible outcomes of the experiment

Given that the two dice are rolled simultaneously.Therefore, the total number of outcomes

=6×6=36
  Now, the possible outcomes to get the sum of 2

=(1,1)

∴P(2)=
    1
    
     36

Possible outcomes to get the sum of 3

=(2,1), (1,2)

∴P(3)=
    2
    
     36
   
   =
    1
    
     18

Possible outcomes to get the sum of 4

=(3,1), (1,3), (2,2)

∴P(4)=
    3
    
     36

Possible outcomes to get the sum of 5

=(4,1), (1,4), (2,3), (3,2)

∴P(5)=
    4
    
     36
   
   =
    1
    9

Possible outcomes to get the sum of 6

=(5,1), (1,5), (2,4), (4,2), (3,3)

∴P(6)=
    5
    
     36

Possible outcomes to get the sum of 7

=(6,1), (1,6), (2,5), (5,2), (4,3), (3,4)

∴P(7)=
    6
    
     36
   
   =
    1
    6

Possible outcomes to get the sum of 8

=(6,2), (2,6), (3,5), (5,3), (4,4)

∴P(8)=
    5
    
     36

Possible outcomes to get the sum of 9

=(6,3), (3,6), (5,4), (4,5)

∴P(9)=
    4
    
     36
   
   =
    1
    9

Possible outcomes to get the sum of 10

=(6,4), (4,6), (5,5)

∴P(10)=
    3
    
     36

Possible outcomes to get the sum of 11

=(6,5), (5,6)

∴P(11)=
    2
    
     36
   
   =
    1
    
     18

Possible outcomes to get the sum of 12

=(6,6)

∴P(12)=
    1
    
     36

Since, none of the above 11 possible outcomes has a probability =

1
    
     11

.Hence, the given argument is false.Hence option (2) is false.

State true or false.

Two dice are rolled simultaneously.

Consider the following table:

A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $= 111$ .

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State true or false.Two dice are rolled simultaneously. Consider the following table: A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability = 1 11 .