Question

You have a 4 sided die and 10 sided die that are rolled 50 times. What is the theoretical probability that the small die is odd, the sum of the numbers is 5, the same # appears on both, the # on the larger die is > than the # on the smaller die.

Answer 1

There are a total of 4*10 = 40 outcomes for the result on the two dice throws here.

a) The probability that the small die is odd is computed here as:
= P(X = 1 or X = 3) = 2/4 = 0.5
Therefore 0.5 is the required probability here.

b) P(sum of the numbers is 5) = P(14, 23, 32, 41) = 4/40 = 0.1
Therefore 0.1 is the required probability here.

c) The probability that same number appears on both is computed here as:
P( 11 or 22 or 33 or 44) = 4/40 = 0.1
Therefore 0.1 is the required probability here.

d) The probability that number on larger die is greater than on smaller die is computed here as:
= P(X = 1, Y > 1) + P(X = 2, Y > 2) + P(X = 3, Y = 3) + P(X = 4, Y > 4)
= (1/4)*(0.9 + 0.8 + 0.7 + 0.6)
= 0.25*(3) = 0.75

Therefore 0.75 is the required probability here.