Target this
Tom, Dick and Harry each have a 10 per cent chance of hitting the bulls-eye with any arrow they fire.
They each put $5 into a can and shoot at the target in the order of Tom first, then Dick, then Harry (and if no one hits the bulls-eye, they cycle through in that same order until someone does.) The first person to hit the bulls-eye wins the money.
What is Harry's chance of winning the money? Express as a percentage to 2 decimal places.
The answer is 29.89.
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1 solution
Consider 1,000 cycles. In 100 of them Tom, who shoots first, hits the bulls-eye and wins the money. In the remaining 900 cycles, Dick, who shoots next, wins the money 90 times. In the remaining 810 cycles, Harry wins the money 81 times, and since the other 729 cycles have no winner the situation "resets". So in 271 cycles where we have a winner, Harry is the winner 81 times. His chance of winning is therefore 81/271 = 29.89%