Logic Puzzle #54

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

Puzzle #54

You have 3 baskets, & each 1 contains exactly 4 balls, each of which is of the same size. Each ball is either red, black, white, or purple, & there is 1 of each color in each basket. If you were blindfolded, & lightly shook each basket so that the balls would be randomly distributed, & then took 1 ball from each basket, what chance is there that you would have exactly 2 red balls, and 1 non-red ball?

Reveal Answer

There are 64 different possible outcomes, & in 9 of these, exactly 2 of the balls will be red — There is thus a slightly better than 14% chance that exactly 2 balls will be red. A much faster way to solve the problem is to look at it this way. There are 3 scenarios where exactly 3 balls are red: 1 2 3 R R X R X R X R R X is any ball that is not red. There is a 4.6875% chance that each of these situations will occur. Take the first 1, for example: 25% chance the first ball is red, multiplied by a 25% chance the second ball is red, multiplied by a 75% chance the third ball is not red. Because there are 3 scenarios where this outcome occurs, you multiply the 4.6875% chance of any 1 occurring by 3, & you get 14.0625%.

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