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?
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.