Question

6 fair 12-sided dice are rolled.

(a)	[3 marks] Find the conditional probability that at least one die lands on 3 given that all 6 dice land on different numbers.

(b)	[2 marks] True or False: If X is the maximum of the 6 numbers from one roll, and Y is the minimum of the 6 numbers from one roll, then X and Y are independent random variables.

Answer 1

Answer:

Given that:

6 fair 12 sided dice are rolled

a) Find the conditional probability that at least one die lands on 3 given that all 6 dice land on different numbers.

The conditional probability that at least one die lands on 3 given that all 6 dice land on different numbers is computed here as

= 1 - Probability that none lands on 3 given that there was a different number on all 6 dice

Therefore 0.5 is the required probability here.

b)  True or False: If X is the maximum of the 6 numbers from one roll, and Y is the minimum of the 6 numbers from one roll, then X and Y are independent random variables.

The above statement is true because the value of X does not affect the value of Y and the value of Y does not affect the value of X.Hence they are independent random variables