The genotype of an organism can be either normal (wild type, W) or mutant (M). Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring. Calculate the probability of a string of the following genotypes in successive generations: WWW.

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Chapter8: Sequences, Series,and Probability
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5c The genotype of an organism can be either normal (wild type, W) or mutant (M). Each generation, a
wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability
0.005 of having a wild type offspring. Calculate the probability of a string of the following genotypes
in successive generations: WWWW.
5D There are three kinds of vegetation in an ecosystem: grass (G), shrubs (S), and trees (T) . Every year,
25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of
trees are converted to shrubs, and 1% of trees are converted to grass; the other transition
probabilities are 0. Calculate the probability ofma plot of land have the following succession of
vegetation from year to year: GSGG.
5E The NACHR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and
open (O) with transition probabilities (per one microsecond): 0.04 (from R to C), 0.07 (from C to R),
0.12 (from C to O) and 0.02 (from O to C); the other transition probabilities are 0. Calculate the
probability of the following string of states: OCCR.
Transcribed Image Text:5c The genotype of an organism can be either normal (wild type, W) or mutant (M). Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring. Calculate the probability of a string of the following genotypes in successive generations: WWWW. 5D There are three kinds of vegetation in an ecosystem: grass (G), shrubs (S), and trees (T) . Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are converted to shrubs, and 1% of trees are converted to grass; the other transition probabilities are 0. Calculate the probability ofma plot of land have the following succession of vegetation from year to year: GSGG. 5E The NACHR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and open (O) with transition probabilities (per one microsecond): 0.04 (from R to C), 0.07 (from C to R), 0.12 (from C to O) and 0.02 (from O to C); the other transition probabilities are 0. Calculate the probability of the following string of states: OCCR.
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