# Tagged: die

## Problem 745

Consider an infinite series of events of rolling a fair six-sided die. Assume that each event is independent of each other. For each of the below, determine its probability.

(1) At least one die lands on the face 5 in the first $n$ rolls.
(2) Exactly $k$ dice land on the face 5 in the first $n \geq k$ rolls.
(3) Every die roll results in the face 5.

## Problem 728

A fair six-sided die is rolled.

(1) What is the conditional probability that the die lands on a prime number given the die lands on an odd number?

(2) What is the conditional probability that the die lands on 1 given the die lands on a prime number?

## Problem 727

Two fair and distinguishable six-sided dice are rolled.

(1) What is the probability that the sum of the upturned faces will equal $5$?

(2) What is the probability that the outcome of the second die is strictly greater than the first die?