Question

Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are rolled and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.

Answer 1

Dice 1

S = {1,2, 3, 4, 5, 6}

Dice 2

S = {1,1,2, 2, 3, 3}

Total possible outcomes when they are rolled

n(S) = 36

Event of sum (2) = A = {(1,1), (1,1)}

n(A) = 2,P(A) = \(\frac{2}{36}\)

Event of sum 3 is B = {(1, 2), (1, 2), (2, 1), (2, 1)}

n(B) = 4, P(B) = \(\frac{n(B)}{n(S)}=\frac{4}{36}\)

Event of sum 4 is C= {(1, 3), (1, 3), (2, 2), (2, 2), (3, 1), (3, 1)}

n(C) = 6

Event of getting the sum 5 is

D = {(2, 3), (2, 3), (3, 2), (3, 2), (4, 1), (4, 1)}

n(D) = 6, P(D) = \(\frac{6}{36}\)

Event of getting the sum 6 is

E = {(3, 3), (3, 3), (4, 2), (4, 2), (5, 1), (5, 1)}

n(E) = 6, P(E) = \(\frac{6}{36}\)

Event of getting the sum 7 is

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

n(F) = 6

P(F) = \(\frac{6}{36}\)

Event of getting the sum 8 is

G = {(5, 3), (5, 3), (6, 2), (6, 2)}

n(G) = 6, P(G) = \(\frac{4}{36}\)

Event of getting the sum 9 is

H = {(6, 3), (6, 3), n(H) = 2