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# In a Single Throw of Two Dice, Find the Probability Of: a Total of at Most 10 - Mathematics

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#### Question

In a single throw of two dice, find the probability of:

a total of at most 10

#### Solution

The  number of possible outcomes is 6xx6=36,  We write them as given below:

1,11,21,,31,41,51,6

2,12,22,32,42,52,6

3,13,23,33,43,53,6

4,14,24,34,44,54,6

5,15,25,35,45,55,6

6,16,26,36,46,56,6

n(s)=36

E= Event of  getting a total of at most 10=

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

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

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

{(5,1)(5,2)(5,3)(5,4)(5,5)}

{(6,1)(6,2)(6,3)(6,4)}

Thereefore total number of favorable ways=33=n(E)

Probability of getting a total of at most 10= (n(E))/(n(s))=33/36=11/12

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