In a game involving dice, Alex and Sam are competing. Sam has tampered with the dice, making the likelihood of rolling any number n equal to n times the likelihood of rolling a 1. According to the game rules, Alex earns a point for every odd number rolled, while Sam earns a point for even numbers. What is the probability that Alex will score a point on a single roll?

Correct answer marked below

\frac{3}{7}

Correct

\frac{4}{7}

\frac{5}{7}

\frac{6}{7}

\frac{7}{8}

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Explanation

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Official Explanation

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Let the probability of rolling a 1 be

\frac{1}{y}

. Therefore, the probabilities for rolling 2, 3, 4, 5, and 6 are

\frac{2}{y}, \frac{3}{y}, \frac{4}{y}, \frac{5}{y}, \frac{6}{y}

respectively. Since these are the only outcomes, their total probability must equal 1: [m]\frac{1}{y} + \frac{2}{y} + \frac{3}{y} + \frac{4}{y} +…

Comments

DiegoJul 31, 2024

Great

What this question tests

Your ability to compute probabilities of single and compound events, including 'at least one' questions.

Forgetting to use the complement for 'at least one', or treating dependent events as independent.