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 (1)8 (2)13? (3)less than or equal to 12?

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Answer 1

Answer:

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#ur Ans

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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

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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  

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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

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