Thread: URGENT : Probability?

There is a 50‐50 chance that the king carries the gene of twins. If he is a carrier, then each princess has a 50‐50 chance of having twins independently. If the king is not a carrier, the princess will not have the disease. Suppose the king has had three princeses without the disease. What is the probability the king is a carrier?

What "disease" are we talking about? The "gene of twins"? Is having twins a disease? Our mother never told my twin brother and me that! (Well, now that I think about it, we were pain sometimes.)

If a king has this horrible twins "disease" gene and has three daughters, the probability none have the "disease" is (1/2)^3= 1/8. Of course, if the king does not have the "disease" that probability is 1. Imagine 800 kings, 400 with the gene, 400 without, all of whom have three daughters. There are a total of 800 "sets" of daughters, 400 from the first group of whom 400/8= 50 do not have twins, 400 from the second group, none of whom have twins. That is a total of 450 sets of daughters who do not have twins, 50 of whose sire was a carrier. The probability a king with three daughters who do not have the "disease" is a carrier is 50/450= 1/9.