SOLUTION: A six-sided die is printed with the numbers 1,2,3,5,8 and 13. Roll the dice once- what is the probability of getting an even number? roll the die twice and add the numbers; what

1, 2, 3, 5, 8, 13

Count the red ones, get 2.  Count them all, get 6.  That's a probability of
2 out of 6, or 2/6, which reduces to 1/3.

 (1,1)  (1,2)  (1,3)  (1,5)  (1,8)  (1,13)  
 
 (2,1)  (2,2)  (2,3)  (2,5)  (2,8)  (2,13)
 
 (3,1)  (3,2)  (3,3)  (3,5)  (3,8)  (3,13) 
 
 (5,1)  (5,2)  (5,3)  (5,5)  (5,8)  (5,13)
 
 (8,1)  (8,2)  (8,3)  (8,5)  (8,8)  (8,13)

(13,1) (13,2) (13,3) (13,5) (13,8) (13,13)

Count the red ones, get 16. Count them all, get 36.  That's a probability of
16 out of 36, or 16/36, which reduces to 4/9.

(a)  The probability is the ratio of favorable outputs to the total outputs.


     In question (a), there are 2 favorable outputs against 6 total outputs.


     You can do the rest.




(b)  In case (b), the total number of all possible outputs is 6*6 = 36.


     Of them, favorable are sums of even and odd outputs, and the number of such outputs (pairs) is 2*4 + 4*2 = 16.


     So, the number of total favorable outputs is  16  against total possible outputs 36.


     THEREFORE, the probability in case  (b)  is  P =  = .

    To answer question (b), it is not necessary to calculate all, each and every of 36 possible outputs individually and separately.


    You can evaluate all necessary numbers for the solution in more simple and cheaper way, spending less efforts.