Daily Math Puzzle: 2026-09-28

4/9 — To win the legendary artifact, there are two distinct sequences of events that lead to a win: **Path 1: Win on the first activation.** This occurs if the first activation of the Orb of Fate shows 'Success'. The probability of 'Success' on any given activation is 1/3 (since there are three faces with equal probability: Success, Failure, Neutral). So, P(Win via Path 1) = 1/3. **Path 2: Win on the second activation.** This path can only occur if the first activation shows 'Neutral', AND then the second activation shows 'Success'. * The probability of the first activation being 'Neutral' is 1/3. * If the first activation is 'Neutral', you proceed to activate the orb a second time. The outcome of this second activation is independent of the first. * The probability of the second activation being 'Success' is also 1/3. To find the probability of both these independent events happening in sequence, we multiply their probabilities: P(Win via Path 2) = P(First is Neutral) × P(Second is Success) = (1/3) × (1/3) = 1/9. Since Path 1 and Path 2 are mutually exclusive (they cannot both happen for the same challenge), the total probability of winning is the sum of their individual probabilities: Total P(Win) = P(Win via Path 1) + P(Win via Path 2) Total P(Win) = 1/3 + 1/9 To add these fractions, we find a common denominator, which is 9: Total P(Win) = 3/9 + 1/9 = 4/9. Therefore, the probability of winning the legendary artifact is 4/9.