Question

Two dice are rolled. Determine the probability of the following. Rolling an even number or a number greater than 10

Answer 1

I hope tye die are rolled simultaneously and you want the proibbility that the Sum of the tow dice will show up your required events.

Let, A: the event that sum of the two numbers apperaed is an even number.

B: the sum of the two numbers appeared is greater than 10.

W have to find P[A or B] = P[]

By theorem of total probability we know,  

Now ,

P[A] = probability that the sum of the apperaed number is an even number.

= probability that either both numbers are odd or both numbers are even

= [Because there are 3 odd and 3 even numbers in a dice ,

=1/2 So probability of a dice showing and odd number = 1/2 and thus 1/4 for two die ]

And P[B] = probability that a score of greater than 10 has apperaed

= P[Sum is either 11 or 12]

Now, total possble combination = (6​6) = 36 . [ such as {1,2},{1,3}......{2,1}.....{6,6}]

Out of which , score can be 11 in two cases : {5,6} and {6,5}

and 12 can appear in only one way : {6,6}

So total 3 cases favourable to event B .

Hence P[B] = 3/36 = 1/12

and P[A B] = P[The score is greater than 10 and an even number]

= P[The score is 12]

= 1/36 [Calculated earlier].

So finally   

  

If you have doubts, or need explanation with different approach, let me know below, I will help you . Thank You.

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