Question

Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is
(a)8
(b)13
(c)Less than or equal to 12

Answer 1

#ur Ans
_________

When we tossed a die , than total number of events ( outcomes ) = 6  , As : {  1 , 2 , 3 , 4 , 5 , 6 }

But when we tossed two dice simultaneously , than total number of events ( outcomes ) =  6 × 6 = 36 

As we can show  all the possible outcomes , As : { 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 }

So,

n ( S  ) = 36

We know that

==> probability P ( E )  =   Total number of desired events n ( E ) /Total number of events n ( S )

a) The probability that the sum of two numbers appearing on the top of the dice is  8

So,

Number of events = { 2 , 6 }, { 3 , 5 }, { 4 , 4 }, { 5 , 3 } ,{ 6 , 2 }

So,

n ( E ) =  5
The probability that the sum of two numbers appearing on the top of the dice is  8 = 5/36 Ans
 ____________________

b ) The probability that the sum of two numbers appearing on the top of the dice is  13

So,

Number of events = 0

Then,

n ( E ) =  0
The probability that the sum of two numbers appearing on the top of the dice is 13= 0/36= 0   Ans 
____________________         

c) The probability that the sum of two numbers appearing on the top of the dice is  less than or equal to 12

So,

Number of events = { 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 }

So,

n ( E ) =  36
The probability that the sum of two numbers appearing on the top of the dice is less than or equal to 12 = 36/36 = 1   Ans
____________________          

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Answer 2

Answer:

The probability that the sum of the two numbers appearing on the top of the dice is

(a) For Sum is 8 = 5/36

(b) For Sum is 13 = 0

(c) For Less than or equal to 12 = 1

Step-by-step explanation:

Two dices are thrown, and the total possible Outcomes =  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)

(a) if Sum = 8

Favourable outcomes = (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5

P(sum is 8) = 5/36

(b) If Sum = 13

Favourable Outcomes = 0

P(sum is 13) = 0

(iii) For sum Less than or equal to 12

Possible outcomes = (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)

P(SUM<=12) =36÷36

                    =1

All outcomes have sum less than or equal to 12.

P(less than or equal to 12) = 1