Question

Roll two dice (one red and one white). Denote their outcomes as X1 and X2. Let...

Roll two dice (one red and one white). Denote their outcomes as X1 and X2. Let T = X1+X2 denote the total, let X1 W X2 denote the maximum and let X1 V X2 denote the minimum. Find the following probabilities: (a) P(X1 ≥ 3|X2 ≤ 4) (b) P(T is prime) (c) P(T ≤ 8|X1 W X2 = 5) (d) P(X1 V X2 ≤ 5|T ≥ 8) (e) P(X1 W X2 ≥ 3|X1 W X2 ≤ 3)

[(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)

(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)

(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)

(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)

(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)]

Where left input is X1 and right one is X2

a) X1 is greater than equal to 3 in 24 cases

X2 is less than four in 24 cases

b) T is prime when either both X1 and X2 are even or odd

X1\ge 3| X2\le 4By above table we can see it happens exactly 18 times

c) T is less than equal to 8, 26 times

Maximum of X1 and X2 is equal to 5, 9 times

out of those 9 times T is less than equal to 8 only 4 times

d) Minimum of X1 and X2 is less than equal to 5, 25 times

T is greater than equal to 8, 15 times

out of these 15 times minimum of X1 and X2 is less than equal to 5, 6 times