Question

a pair of dice is tossed once find the probability of getting a total of 2a total of 5 and even number as a sum same number on each dice ​

Answer 1

Given :

A pair of dice is tossed once.

To Find :

          ( a )The probability of getting a total of 5.

          ( b ) Even number as a sum .

          ( c ) Same number on each dice ​.

Solution :

• When a pair of dice is thrown , the possible outcomes are :

        $(1, 1) ; (1, 2) ; (1, 3) ; (1, 4) ; (1, 5) ; (1, 6)$

        $(2, 1) ; (2, 2) ; (2, 3) ; (2, 4) ; (2, 5) ; (2, 6)$

        $(3, 1) ; (3, 2) ; (3, 3) ; (3, 4) ; (3, 5) ; (3, 6)$

        $(4, 1) ; (4, 2) ; (4, 3) ; (4, 4) ; (4, 5) ; (4, 6)$

        $(5, 1) ; (5, 2) ; (5, 3) ; (5, 4) ; (5, 5) ; (5, 6)$

        $(6, 1) ; (6 ,2) ; (6, 3) ; (6, 4) ; (6, 5) ; (6, 6)$

There are a total of 36 possible outcomes.

     ( a ) The probability of getting a total of 5.

• The outcomes should be ( 1, 4 ) , ( 2 , 3 ) , ( 3, 2 ) , ( 4 ,  1 )

• Therefore,
• probability of getting a total of 5 = 4/36 = 1/9

     ( b ) Even number as sum .

• Outcomes can either be both even or both odd.
• Such outcomes are :
• ( 1, 1 ) , ( 1 , 3 ) , ( 2, 2 ) , ( 2, 4 ) etc .
• It is half of the total outcomes.

• probability of getting  even number as sum = 18/36 = 1/2

   

   ( c ) Same number on each dice ​.

• Outcomes are ( 1 , 1 ) ,( 2 , 2 ) , ( 3, 3 ) , ( 4, 4 ) , ( 5, 5) , ( 6 , 6 ).
• Therefore there are 6 possible outcomes.

• probability of getting  same number on each dice = 6 / 36 = 1/6

Therefore the probability of getting a total of 5 = 1/9 ,

probability of getting  even number as sum =  1/2 and

probability of getting  same number on each dice = 1/6.

Answer 2

Answer:

        ( a )The probability of getting a total of 5.

        ( b ) Even number as a sum .

        ( c ) Same number on each dice ​.

Solution :

When a pair of dice is thrown , the possible outcomes are :  

                                                                                                                                   There are a total of 36 possible outcomes.

   ( a ) The probability of getting a total of 5.

The outcomes should be ( 1, 4 ) , ( 2 , 3 ) , ( 3, 2 ) , ( 4 ,  1 )

Therefore,

   ( a )The probability of getting a total of 5.

        ( b ) Even number as a sum .

        ( c ) Same number on each dice ​.

Solution :

When a pair of dice is thrown , the possible outcomes are :

     

     

     

     

     

     

There are a total of 36 possible outcomes.

   ( a ) The probability of getting a total of 5.

The outcomes should be ( 1, 4 ) , ( 2 , 3 ) , ( 3, 2 ) , ( 4 ,  1 )

Therefore,

probability of getting a total of 5 = 4/36 = 1/9

   ( b ) Even number as sum .

Outcomes can either be both even or both odd.

Such outcomes are :

( 1, 1 ) , ( 1 , 3 ) , ( 2, 2 ) , ( 2, 4 ) etc .

It is half of the total outcomes.

probability of getting  even number as sum = 18/36 = 1/2

 

 ( c ) Same number on each dice ​.

Outcomes are ( 1 , 1 ) ,( 2 , 2 ) , ( 3, 3 ) , ( 4, 4 ) , ( 5, 5) , ( 6 , 6 ).

Therefore there are 6 possible outcomes.

probability of getting  same number on each dice = 6 / 36 = 1/6

Therefore the probability of getting a total of 5 = 1/9 ,

probability of getting  even number as sum =  1/2 and

   (a) probability of getting  same number on each dice = 1/6.

probability of getting a total of 5 = 4/36 = 1/9

   ( b ) Even number as sum .

Outcomes can either be both even or both odd.

Such outcomes are :

( 1, 1 ) , ( 1 , 3 ) , ( 2, 2 ) , ( 2, 4 ) etc .

It is half of the total outcomes.

probability of getting  even number as sum = 18/36 = 1/2

 

 ( c ) Same number on each dice ​.

Outcomes are ( 1 , 1 ) ,( 2 , 2 ) , ( 3, 3 ) , ( 4, 4 ) , ( 5, 5) , ( 6 , 6 ).

Therefore there are 6 possible outcomes.

probability of getting  same number on each dice = 6 / 36 = 1/6

Therefore the probability of getting a total of 5 = 1/9 ,

probability of getting  even number as sum =  1/2 and

probability of getting  same number on each dice = 1/6.

        ( b ) Even number as a sum .

        ( c ) Same number on each dice ​.

Step-by-step explanation:

When a pair of dice is thrown , the possible outcomes                                There are a total of 36 possible outcomes.

The outcomes should be ( 1, 4 ) , ( 2 , 3 ) , ( 3, 2 ) , ( 4 ,  1 )                                                                  (a)                                                                                                                                                                

Therefore,

probability of getting a total of 5 = 4/36 = 1/9

   ( b ) Even number as sum .

Outcomes can either be both even or both odd.

Such outcomes are :

( 1, 1 ) , ( 1 , 3 ) , ( 2, 2 ) , ( 2, 4 ) etc .

It is half of the total outcomes.

probability of getting  even number as sum = 18/36 = 1/2

 

 ( c ) Same number on each dice ​.

Outcomes are ( 1 , 1 ) ,( 2 , 2 ) , ( 3, 3 ) , ( 4, 4 ) , ( 5, 5) , ( 6 , 6 ).

Therefore there are 6 possible outcomes.

probability of getting  same number on each dice = 6 / 36 = 1/6

Therefore the probability of getting a total of 5 = 1/9 ,

probability of getting  even number as sum =  1/2 and

probability of getting  same number on each dice = 1/6.

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