   SEARCH HOME Math Central Quandaries & Queries  Question from Brian: Two participants are alternatively selecting eggs from a basket of 6 hard-boiled eggs and 6 uncooked eggs. Alternatively they are smashing the eggs on their foreheads. One participant gets 4 hard boiled eggs in a row and the other person gets 4 uncooked eggs in a row. What is the probability of this occurring (I watched this happen). Thank you Brian Hi Brian,

At the start there are 12 eggs in the basket, 6 hard-boiled and 6 uncooked so the probability that the first egg selected is hard-boiled is $\frac{6}{12}.$ Now there are 11 eggs in the basket, 5 hard-boiled and 6 uncooked so the probability that the second egg selected is uncooked given that the first egg was hard-boiled is $\frac{6}{11}.$ Thus the probability that the first egg selected is hard-boiled AND the second egg selected is uncooked given that the first egg was hard-boiled is $\frac{6}{12} \times \frac{6}{11}.$

The pattern continues, the probability that the third egg selected is hard-boiled given that first egg selected is hard-boiled AND the second egg selected is uncooked given that the first egg was hard-boiled is $\frac{6}{12} \times \frac{6}{11} \times \frac{5}{10}.$

Continue for 8 eggs.

Penny      Math Central is supported by the University of Regina and the Imperial Oil Foundation.