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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?
Solution
Total no. of outcomes when both cubes are rolled = 6 × 6 = 36 which are
{ (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) }
E ⟶ event of getting same no. on each cube
No. of favourable outcomes = 6 which are
{ (1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}
Probability, P(E) =`"No.of favorable outcomes"/"Total no.of possible outcomes"`
=6/36 =1/6
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