Two rolls of a fair die. Let x and y be the results of the...

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Two rolls of a fair die. Let x and y be the results of the tworolls, and let z = x + y.
(a) Find P[x = 4, y = 3], P[x > 3, y = 5].
(b) Find P[z = 7], P[z = 5], P[z = 3].
(c) Find the probability that at least one 6 appears given thatz = 8.
(d) Find the probability that x = 6 given that z > 8.
(e) Find the probability that z = 7 given that at least one 4was rolled. (f) Find the probability that z > 7 given that y =4.

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Following is the event space for the result of the two rolls of a fair diex first roll y second roll zxy xFirst Roll ySecond roll zxy 1 1 1 2 2 1 2 3 3 1 3 4 4 1 4 5 5 1 5 6 6 1 6 7 7 2 1 3 8 2 2 4 9 2 3 5 10 2 4 6 11 2 5 7 12 2 6 8 13 3 1 4 14 3 2 5 15 3 3 6 16 3 4 7 17 3 5 8 18 3 6 9 19 4 1 5 20 4 2 6 21 4 3 7 22 4 4 8 23 4 5 9 24 4 6 10 25 5 1 6 26 5 2 7 27 5 3 8 28 5 4 9 29 5 5 10 30 5 6 11 31 6 1 7 32 6 2 8 33 6 3 9 34 6 4 10 35 6 5 11 36 6 6 12 Total number of events 36 a Px4 y3 From the above table Rows that favor x4 y3 is xFirst Roll ySecond roll zxy 21 4 3 7 Number of event favoring Event x4 y3 1 Px4 y3 Number of event favoring Event x4 y3 Total number of events 136 Px4 y3 136 Px 3 y 5 From the table rows See Answer

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