One six in four rolls versus double six in 24

Question

Which bet is more likely to win? Bet 1: roll one fair die four times and get at least one six. Bet 2: roll two fair dice $24$ times and get a double six at least once. Answer $1$ , $2$ , or $3$ if they are equally likely.

Short answer

$1$ . Bet 1 wins with probability $1-(5/6)^4\approx0.518$ , while Bet 2 wins with probability $1-(35/36)^{24}\approx0.491$ (the classic de Méré problem).

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

Counting and Combinatorics
Expectation, Mean, and Variance
Sample Spaces, Events, and the Probability Axioms

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