Problem 5

The Koozebanian Fazoob has three genders, ma, na and muna, each with equal probability of being born. Fazoobs are oviparous and large clutches of eggs are incubated in hatching cells. During one particular day, in a certain cell, one hundred eggs hatch. There are twenty more ma hatchlings than na hatchlings and the total number of ma and na hatchlings is four times larger than the number of muna hatchlings. One more egg hatches overnight and in the morning a brood mother selects one of the one hundred and one hatchlings at random for cleaning; it happens to be a ma. What is the probability that the egg that hatched overnight contained a ma?

Please enter your answer as a fraction in its lowest terms, e.g. if you think that the answer is 0.8 then enter 4/5 with no spaces.