Question

The faces of a red cube and a yellow cube are numbered from 1 to 6. Both cubes are rolled. What is the probability that the top face of each cube will have the same number?

Answer 1

SOLUTION :    

Given : The faces of a red cube and a yellow cube are numbered from 1 to 6

If we throw two cubes then there possible outcomes are as follows:

{(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)}

Total number of outcomes when both cubes are rolled = 6 x 6 = 36

Let E = Event of getting same number on each cube

same number on each cube = { (1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}

No. of favorable outcomes = 6

Required probability P(E)= Number of favourable outcomes / total number of outcomes

P(E) = 6/36 = ⅙  

Hence, the Required probability of getting same number on each cube , P(E) = ⅙  

HOPE THIS ANSWER WILL HELP  YOU….

Answer 2

the dice/cubes can appear 36 ways (6 * 6) 

of these, 6 pairs are doubles... 

6/36 = 1/6