Math Brain Teaser #13

From Billy-B's legendary 1001 Puzzle Collection — preserved on Puzz.com since 1998.

Puzzle #13

Anyone telesent (like being teleported or "beamed up") to Space Station Exray will arrive in pod A, B, or C. You are twice as likely to arrive in pod A than in pod B, & three times as likely to arrive in pod B than pod C. How likely is it that you will arrive in pods B, C, & A, in that order, the only three times that you are telesent to Space Station Exray? You may express your answer as a fraction or as a percentage.

Reveal Answer

The answer is 9/500, or 1.8%. The problem can be set up algebraically — For each trip, there is a 100% chance that you will arrive in pod A, B, or C. Let X be the chance that you arrive in pod A, & since it is twice as likely that you will arrive in A than B, there is only half the chance that you will arrive in B than A. So B is 1/2 X. By the same reasoning, there is only 1/6 the chance you would arrive in C than A, so C is 1/6 X. The equation thus looks like this: 100 = X + 1/2X + 1/6X. X=60, so A = 60, B = 30, & C = 10. These numbers correspond to the % chances you would arrive in each pod. The answer is found by multiplying these three percentages together (i.e. .3 x .1 x .6). There is only a 1.8% chance that you would arrive in these 3 pods in this particular order for your only 3 trips to Exray.

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