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Did You Work It Out? The Solution to Our Riddle from the E-News Issue of July 2014

Who predicts the right sequence?

Probability calculation, riddle, brain teaser, e-news, solution, eggs
Which sequence of colored eggs will probably be observed first?

In a laying battery, half the chickens lay brown eggs and the other half lay white eggs. These are transported individually and in random order to the packing station on a conveyor belt.

Sarah and Tim work sorting the eggs at the packing station. In order to make their work a little more entertaining, they try to predict certain sequences. The person whose prediction is confirmed first, wins. Sarah predicts white, brown, brown; Tim says brown, brown, white.

Who has the greater chance of winning and how great is it?

Solution

Tim only wins if two brown eggs are delivered first. Sooner or later, a white egg will follow, e.g. bbw, bbbw, bbbbw, etc. Tim wins in the case of any of these sequences. The probability for two brown eggs to be delivered first is 1/2 * 1/2 = 1/4.

In all other cases, Sarah wins, as the sequence bb is always preceded by a white egg. Sarah therefore has a greater chance (75 %) of winning the bet.