Flip five coins, or draw from a bag of sovereigns — two riddles in one
First: toss five pennies at once. What are the odds that at least four of them land showing the same face, all heads or all tails? Second: a bag holds three sovereigns and one shilling, and you may draw one coin blindfolded, keeping whatever you get. How much should you fairly pay for that single draw?
Reveal the answer
3/8 for the first: the chance of getting exactly four or five matching faces is 6 out of 32 for heads plus 6 out of 32 for tails, which is 12/32, or 3/8. For the second, three sovereigns worth 20 shillings each plus one shilling total 61 shillings across 4 coins, so a fair price for one random draw is the average, 15 shillings and 3 pence. Both are Puzzle No. 30, 'Two Questions in Probabilities,' from Henry Dudeney's 1917 Amusements in Mathematics.
— Henry Ernest Dudeney, Amusements in Mathematics — Puzzle No. 30, 1917