Question

Two dices, one blue and one grey are thrown at the same time. Write down all the
possible out comes. What is the probability that the sum of the two numbers appearing on
the top of the dice is
(1) 8 (2) less than or equal to 12 ?​

Answer 1

f two dices are thrown, the total possible outcomes will be:

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

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

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

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

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

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

now, total possible outcomes are 36

(i) outcomes = (2+6) , (3+5), (4+4) , (5+3), (6+2)

P(SUM=8) = 5/36

(ii) outcomes= 0

P(SUM=13) = 0/36=0

(iii) 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

Hope it helps buddy

mark the brainliest

Answer 2

$\huge\underline\mathfrak\pink{♡Answer♡}$

➡️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  

____________________         

➡️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