Critical Thinking Consider two independent populations for which the proportion of successes in the first population is
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- Family Planning A intend to have two children. What is tie probability that they will have child of each sex? The French mathematician IY Alembert analyzed this problem (incorrectly) by reasoning that three outcomes are possible: or two girls, or one child of each sex. He concluded that probability of having of each sex is mistakenly assuming that three outcomes are likely. (a) Model this problem with a pair of coins (using "heads" for boys and "tails" for girls). or write a program to model of problem. perform the experiment 40 mere times. Counting the number of boy-girl combinations. Estimate the probability of having child of each. (b) Calculate the correct probability of having one child of each sex and compare this with your result from part (a).arrow_forwardShow the sample space of the experiment: toss a fair coin three times.arrow_forwardYou toss two six-sided dice. What is the probability that the total of the two dice is 5?arrow_forward
- Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?arrow_forwardSnake Eyes What ¡s the probability of rolling snake eyes ("double ones") three times in a row?arrow_forward
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