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Two MIT math graduates bump into each other at Fairway on the upper west side. They hadn't seen each other in over 20 years. The first grad says to the second: "how have you been?" Second: "Great! I got married and I have three daughters now" First: "Really? how old are they?" Second: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there.." First: "Right, ok.. oh wait.. hmmmm.., I still don't know" second: "Oh sorry, the oldest one just started to play the piano" First: "Wonderful! my oldest is the same age!" Problem: How old are the daughters?
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Consider two linked autosomal genes. The dominant allele C of the first gene causes cataracts of the eye, whereas its recessive allele produces normal eyes. The dominant allele P causes polydactyly (an extra finger) whereas its allele (p) produces a normal number of fingers. A man with cataracts and normal fingers marries a woman with polydactyly and normal eyes. Their son has both polydactyly and cataracts and he marries a woman with neither trait. What is the probability that their first child will have cataracts and polydactyly?
