of rolling two dice successively, find the probability that: a) the sum of the dice is even, knowing that the first die indicates 4. b) the sum of the dice is even, knowing that the first die indicates an even number. c) the sum of the dice is 10, knowing that the first die indicates an even number.

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In the random experiment consisting of rolling two dice successively, find the probability that:
a) the sum of the dice is even, knowing that the first die
indicates 4.
b) the sum of the dice is even, knowing that the first die
indicates an even number.
c) the sum of the dice is 10, knowing that the first die
indicates an even number.
d) the sum of the dice is 10, knowing that the first die
indicates an odd number.
e) the sum of the dice is 10, knowing that the first die
indicates 3.

Expert Solution
Step 1: We have given that

In the random experiment consisting of rolling two dice successively.

Sample space 

S={ (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) }

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