Question

the probability of getting two different numbers when two regular dice are rolled is??

Answer 1

(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 Possible outxomes=36
Total favourable=30

probability= 30/36
=5/6

Answer 2

Total number of possible outcomes when two dice are rolled n(S) = 6^2

                                                                                                               = 36.


Let A be the event of getting the same numbers when two dice are rolled:

n(A) = {1,1},{2,2},{3,3},{4,4},{5,5},{6,6}.

       = 6.


Therefore the required probability P(A) = n(A)/n(S)

                                                                   = 6/36

                                                                   = 1/6.



Now,

the probability of getting different numbers when two dice are rolled.

=  1 - P(A)

= 1 - 1/6

= 5/6.


Therefore the required probability = 5/6.


Hope this helps!