Sum of 100 hundred-sided dice divisible by 100

Question

One hundred fair dice, each with faces $1$ to $100$ , are thrown together. What is the probability that the total is a multiple of $100$ ?

Short answer

$1/100$ . Condition on the first $99$ dice. Whatever their sum, exactly one face of the last die makes the total divisible by $100$ , so the probability is $\tfrac1{100}$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Conditional Probability, Total Probability, and Bayes' Rule
Counting and Combinatorics
Expectation, Mean, and Variance

Start with a free lesson: Expectation, Variance and Covariance is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free