Question

Problem #3: 5 fair 12-sided dice are rolled. (a) [3 marks] Find the conditional probability that at least one die lands on 3 given that all 5 dice land on different numbers. 6) [2 marks] True or False: If X is the maximum of the 5 numbers from one roll, and Y is the minimum of the 5 numbers from one roll, then X and Y are independent random variables.

Answer 1

a)The conditional probability that at least one die lands on 3 given that all 5 dice land on different numbers=$\frac{1*^{11}C_4}{^{12}C_5}$=$\frac{\frac{11!}{7!4!}}{\frac{12!}{7!5!}}=\frac{5}{12}$

b)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 .