Dice roll probability distribution

Question

Let a fair die be rolled 2 times. Let’s assume that the 2 rolls are independent. Let X and Y be the outcomes of the first and second rolls, respectively.

 

a. What is the probability distribution of X+Y? That is, create a table that contains each unique possible value of X+Y (each value only listed once) and each possibility’s corresponding probability

 

b. What is the probability that X+Y is greater or equal to 1o?

Answer 1

X= 1st roll→     1         2      3      4      5     6    

 

                  1  (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)     a.) 1+1=2 ( the sum of "2" happens 1X) =1/36

 

                  2  (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)          1+2=3 (the sum of "3" happens 2X) = 2/36

Y=2nd         

Roll     ↓     3  (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)          1+3=4 (the sum of "4" happens 3X) = 3/36

 

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

       

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

     

                  6  (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)          1+6=7

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                                                                            b.) P(X+Y greater than10)=3/36

                                                                                (because you can have 5+6, 6+5, 6+6)