Random mutation of cells. Chance (Spring 2010) presented an article on the random mutation...

Random mutation of cells. Chance (Spring 2010) presented an article on the random mutation hypothesis developed by microbiologists. Under this hypothesis, when a wild-type organic cell (e.g., a bacteria cell) divides, there is a chance that at least one of the two “daughter” cells is a mutant. When a mutant cell divides, both offspring will be mutant. The schematic below shows a possible pedigree from a single cell that has divided. Note that one “daughter” cell is mutant (o) and one is a normal cell (o).

a.  Consider a single, normal cell that divides into two offspring. List the different possible pedigrees.

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b.  Assume that a “daughter” cell is equally likely to be mutant or normal. What is the probability that a single, normal cell that divides into two offspring will result in at least one mutant cell?

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c.  Now assume that the probability of a mutant “daughter” cell is .2. What is the probability that a single, normal cell that divides into two offspring will result in at least one mutant cell?

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d.  The schematic below shows a possible second-generation pedigree from a single cell that has divided. Note that the first generation mutant cell automatically produces two mutant cells in the second generation. List the different possible second generation pedigrees. (Hint: Use your answer to part a.)

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e.  Assume that a “daughter” cell is equally likely to be mutant or normal. What is the probability that a single, normal cell that divides into two offspring will result in at least one mutant cell after the second generation?