question_answer

Two different dice are rolled together. Find the probability of getting:

(i) the sum of numbers on two dice to be 5.

(ii) even numbers on both dice.

Answer:

Total possible outcomes when two dices are rolled together \[=36\]

(i) Let \[{{E}_{1}}\]be the event of getting the sum of 5 on two dice.

Then, the favourable outcomes are (2, 3), (3, 2), (1, 4), (4,1).

Number of favourable outcomes \[=4\]

\[\therefore \] P (getting the sum of 5) \[=P({{E}_{1}})=\frac{4}{36}=\frac{1}{9}\]

(ii) Let \[{{E}_{2}}\] be the event of getting even numbers on both dice.

Then, the favourable outcomes are (2, 2), (2, 4), (2, 6), (4, 2), (4, 4) (4, 6), (6, 2), (6, 4), (6, 6)

Number of favourable outcomes \[=9\]

\[\therefore \] P (getting even numbers on both dice) \[=P({{E}_{2}})=\frac{9}{36}=\frac{1}{4}\]