Question

A pair of dice is rolled and the sum of the dice is recorded, determine the probability that:
a) The sum is greater than 5 given the first dice is a 4.
b) The sum is greater than 9 given the second dice is a 6.
c)The sum is even given the second dice is a 4
d) The sum is odd given the first dice is a 3
e) A double is rolled given neither dice is a 4
f)A double is not rolled given the sum is greater than 10
g)The sum is less than 3 given the first dice is a 2
h)The sum is greater than 10 given the first dice is a 3

Answer 1

a) The first dice is 4. In order to make the sum greater than 5, the second dice can show any number except 1. the probability that the dice will show any number except 1 is = 5/6

The probability that the sum is greater than 5 given that the first dice is a 4 is = 5/6.

b) The second dice is 6. In order to make the sum greater than 9, the second dice should show a number greater than 3. The probability that the dice will show a number greater than 3 is = 3/6 = 1/2

The probability that the sum is greater than 9 given that the second dice is a 6 is = 1/2.

c) Given the second dice is 4, the sum will be even if the first dice is also even. The probability that the first dice will be even is = 1/2

The probability that the sum will be even given that the second dice is a 4 is = 1/2.

d) Given the first dice is 3, the sum will be odd if the second dice is even. The probability that the second dice will be even is = 1/2

The probability that the sum will be odd given that the first dice is a 3 is = 1/2.

e) Neither dice is a 4. Which means the double outcome can only be (1,1), (2,2), (3,3),(5,5) and (6,6).

The probability that the outcome will be a double given that none of them is a 4 is = 5/36

f) The sum is greater than 10. The possible cases are (5,6) , (6,5) and (6,6).

Only (6,6) among them is a double.

The probability that a double is not rolled is = 2/3

g) If the first die is a 2, then the sum can never be less than 3 because the least value of the sum that is possible is 3. If we want the sum to be less than 3, then it is not possible.

The probability that the sum is less than 3 given that the first die is 2 is = 0

h) The first dice is 3. The second dice can have a maximum value of 6. That would make the sum 9. So, the sum can never be more than 10.

The probability that the sum will be greater than 10 given the first dice is a 3 is = 0

Thank You!! Please Upvote!!