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The challenge: The odds of selecting the highest number seem to be one in three Or are they Is there a strategy by which you can improve the odds Hint: Find a system by plotting out specific number combinations Chance predicts victory one-third of the time But there is a better strategy to improve your odds The following strategy changes the odds from one-in-three (33 percent) to one-in-two (50 percent) Here s how one candidate described the system: Take the first index card and discard it Make a note of the number, but no matter how high it is, throw it away Now pick the next card (it doesn t matter which) If the number on the second index card has a higher number than the first, retain the second index card If the number on the second index card is lower than the first number, discard that one and select the third index card By way of proof, consider the permutations To really test this strategy, let s assume that the cards are marked A, B, and C The first card, A, will always be discarded, so let s give it the highest value Let s say the three index cards have numbers of 150, 25, and 50 Here s a chart that demonstrates the possible outcomes The first column will always be discarded Column 2 represents the second choice, and column 3 is the third card, which you may or may not get to Here are the six possible outcomes:
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A 150 150 25 50 50 25
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B 25 50 50 150 25 150
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C 50 25 150 25 150 50
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Step Discard A, discard B, keep C Discard A, discard B, keep C Discard A, keep B, ignore C Discard A, keep B, ignore C Discard A, discard B, keep C Discard A, keep B, ignore C
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Outcome Lose Lose Lose Win Win Win
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Six possible combinations yield three wins and three losses: odds of one in two Plug in any numbers It doesn t matter Solution: Pick one card, note the number, and discard it If the number on the second card is higher, keep it If it s lower, discard it in favor of the third card
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107 IT S A GIRL
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A straightforward probability puzzle that has been around for years, yet continues to perplex
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You meet a stranger on the street, and ask how many children he has He truthfully says two You ask, Is at least one of them a girl He truthfully says yes What is the probability that the other one is a girl
Before diving into a response, listen to the question Repeat it once or twice By now your ears should be alert to a peculiar phrase such as at least Ask yourself what that at least implies If you don t, the obvious answer, of course, is 50-50 And, of course, the intuitive answer is wrong Consider the four permutations:
Child 1
1 Girl 2 Girl 3 Boy 4 Boy
Child 2
Girl Boy Girl Boy
The condition at least one is a girl eliminates only condition 4 There are three ways in which at least one of them could be a girl And as a sibling of a girl in those three permutations, where there is girl, boy, or another boy, the chance of that sibling being a girl is only one out of three A candidate explains: The key is that we didn t specify which child was a girl, so it can be either one If we had said instead, The oldest child is a girl;
PROBABILITY PUZZLES
what is the chance that the other one is a girl the odds would be 50-50 But we just specified that at least one was a girl, so we don t know which it is and whether her sibling is a boy or a girl And this means that the chances of that sibling being a girl are one out of three Solution: One-third
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