24. Two fair dice are thrown simultaneously. Find the probability that one die shows the value higher than the other.
Sample space S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,4) (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)}
Event of getting higher number in one die are E= [ (5, 3)(5, 4)(6, 1)(6, 2)(6, 3)(6, 4)(6, 5)]
n(E) = 15
∴ Probability = (n(E)/n(S)) = (15/36) = (5/12)
Sample space S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,4) (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)}
Event of getting higher number in one die are E= [ (5, 3)(5, 4)(6, 1)(6, 2)(6, 3)(6, 4)(6, 5)]
n(E) = 15
∴ Probability = (n(E)/n(S)) = (15/36) = (5/12)
Sample space S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,4) (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)}
Event of getting higher number in one die are E= [ (5, 3)(5, 4)(6, 1)(6, 2)(6, 3)(6, 4)(6, 5)]
n(E) = 15
∴ Probability = (n(E)/n(S)) = (15/36) = (5/12)