Question

. In two dice game, the player take turns to roll both
dice, they can roll as many times as they want in one
turn. A player scores the sum of the two dice thrown
and gradually reaches a higher score as they continue
to roll. If a single number 1 is thrown on either die,
the score for that whole turn is lost. Two dice are
thrown simultaneously.
What is the probability of getting the sum as an
even number

Answer 1

Answer:

(i) All possible outcome are given as below:

(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)

Number of all possible outcomes in all case,

n S( ) = = 6 6 # 36

Favorable outcome are $ . 2 4, , 6 8, , 10, 12 . We may get

as follows

{(1, 1), (1, 3), (3, 1), (2, 2), (1, 5), (5, 1), (2, 4), (4, 2),

(3, 3), (2, 6), (6, 2), (3, 5), (5, 3), (4, 4), (6, 4), (4, 6),

(5, 5), (6, 6)}

Thus number of favourable outcomes,

n E( )1 = 18

P(sum as an even number), = 18/36

=1/2 ans

Answer 2

Answer:

(i) All possible outcome are given as below:

(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)

Number of all possible outcomes in all case,

n S( ) = = 6 6 # 36

Favorable outcome are $ . 2 4, , 6 8, , 10, 12 . We may get

as follows

{(1, 1), (1, 3), (3, 1), (2, 2), (1, 5), (5, 1), (2, 4), (4, 2),

(3, 3), (2, 6), (6, 2), (3, 5), (5, 3), (4, 4), (6, 4), (4, 6),

(5, 5), (6, 6)}

Thus number of favourable outcomes,

n E( )1 = 18

P(sum as an even number), = 18/36

=1/2 ans

Explanation: