There is one spot at one side of the cube, two on another side, three

1.	There is one spot at one side of the cube, two on another side, three on the third side and so on. There are spots on all the six faces; in this order. Another cube which is marked in the same way is taken.a. If both the cubes are thrown, what is the probability that the total number of spots on the upper faces is 6?b. What is the probability that the sum of the spots on the upper faces is 9?c. What is the probability that the sum of the spots be one?d. What is the probability that the sum of the spots be a prime number?
Answer» Total number of pairs 6 x 6 = 36 a. Pairs of spots with total number 6 are (1,5) (2,4) (3,3) (4,2) (5,1) ∴ Probability = \(\frac{5}{36}\) b. Pairs with 9, (3,6) (4,5) (5,4) (6,3) ∴ Probability = \(\frac{4}{36}=\frac{1}{9}\) c. Probability to be 1 = \(\frac{0}{36}=0\) d. Pairs with total number of spots as prime number (1,1) (1,2) (1,4) (1,6) (2,1) (2,3) (2,5) (3,2) (3,4) (4,1) (4,3) (5,2) (5,6) (6,1) (6,5) ∴ Probability = \(\frac{15}{36}\)

There is one spot at one side of the cube, two on another side, three on the third side and so on. There are spots on all the six faces; in this order. Another cube which is marked in the same way is taken.a. If both the cubes are thrown, what is the probability that the total number of spots on the upper faces is 6?b. What is the probability that the sum of the spots on the upper faces is 9?c. What is the probability that the sum of the spots be one?d. What is the probability that the sum of the spots be a prime number?

Answer»

Total number of pairs 6 x 6 = 36

a. Pairs of spots with total number 6 are (1,5) (2,4) (3,3) (4,2) (5,1)

∴ Probability = \(\frac{5}{36}\)

b. Pairs with 9, (3,6) (4,5) (5,4) (6,3)

∴ Probability = \(\frac{4}{36}=\frac{1}{9}\)

c. Probability to be 1 = \(\frac{0}{36}=0\)

d. Pairs with total number of spots as prime number (1,1) (1,2) (1,4) (1,6) (2,1) (2,3) (2,5) (3,2) (3,4) (4,1) (4,3) (5,2) (5,6) (6,1) (6,5)

∴ Probability = \(\frac{15}{36}\)