A die was rolled twice. Find the probability (and provide the answers in the for

Question

A die was rolled twice. Find the probability (and provide the answers in the form of simple fractions) that the number of points on the first roll is greater than the number of points on the second roll________________ the number of points on the first roll is less than the number of points on the second roll__________ the number of points on the first roll is equal to the number of points on the second roll_______________ A die was rolled 6 times. Find the probability that the number of rolled points never repeated_________________.

Explanation / Answer

a) Let A be the event of getting points in first roll greater than second roll.

A = { (6,1), (6,2) , (6,3), (6,4), (6,5), (5,1) , (5,2), (5,3), (5,4), (4,1), (4,2), (4,3), (3,1), (3,2), (2,1)}

n(A) = 15

n(T) = total possible outcomes = 36

P(A) = n(A) / n(T) = 15/36 = 5/12

b) Let B be the event of getting points in first roll lesser than second roll.

B = { (1,2), (1,3), (1,4),(1,5),(1,6), (2,3), (2,4), (2,5), (2,6), (3,4), (3,5), (3,6), (4,5), (4,6), (5,6)}

n(B) = 15

n(T) = total possible outcomes = 36

P(B) = n(B) / n(T) = 15/36 = 5/12

c) Let C be the event of getting equal points on both dies.

C = { (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

n(C) = 6

n(T) = total possible outcomes = 36

P(C) = n(C) / n(T) = 6/36 = 1/6

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