MATH 418 December 2008. Page 2 out of 8
1. [15/100] A rare inherited genetic disease behaves as follows. For people with the gene,
no symptoms arise at all with probability 1 −p, and symptoms appear with probability p
at age 50. Charles is 49. His father Arthur (who is 80) and his sister Belinda (who is 52)
have no symptoms. However Arthur’s father Zoltan did have symptoms.
Because the disease is rare, you can neglect the possibility that Zoltan had 2 copies
of the gene, or that Arthur’s wife or mother had any copies of the gene. People without
the gene never exhibit symptoms.
What is the probability that Charles will exhibit symptoms next year?
