@alisonkiddle@mathstodon.xyz Probabilities are: (½)¹⁰ vs (⅙)⁴ For concise notation, I'll invert them: 2¹⁰ vs 6⁴ We can decompose the right side: (2 * 3)⁴ = 2⁴ * 3⁴ We have 2s exp. so again can reduce both sides: 2⁶ vs 3⁴ Again decomposing: 2³ * 2³ = 8 * 8 vs 9 * 9 We see that the right side is bigger, so when we invert them, the left side is bigger i.e. 10 coin tosses for same side has higher probability: (½)¹⁰ > (⅙)⁴