Worked solution
Compare the two opening dice events
Which is more likely: getting at least one six in 4 rolls of one die, or getting at least one double six in 24 rolls of two dice?
CJC · Lecture · Exploration Activity
Count the complement of no six in four rolls
Assume fair dice and independent rolls. A single roll misses six with probability 5/6, so the chance of at least one six in four rolls is .
Count the complement of no double six in twenty-four rolls
A pair of independent fair dice shows double six with probability 1/36. Thus the chance of at least one double six in 24 rolls is .
Compare the probabilities
The first event is more likely: about 51.8%versus 49.1%. The opening source poses the question without a worked answer; these calculations are supplementary. Multiplying the number of rolls by the one-roll success probability is not the probability of at least one success.
Common mistakes
State the fair-dice and independent-roll assumptions. Count at least one success using the complement of no successes, not by adding overlapping success events.