Solutions Modeling Dynamics of Life 3ed Adler - Chapter 6.3

6.3.1 For the given sets A and B, find A B, A B, and ... (the complement of A). A and B are subsets of the set S={0, 1, 2, 3, 4}. A={0, 1, 2} and B={0, 2, 4}.
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6.3.2 For the given sets A and B, find A B, A B, and ... (the complement of A). A and B are subsets of the set S={0, 1, 2, 3, 4, 5}. A={0, 1, 2} and B={0, 2, 4, 5}.
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6.3.3 For the given sets A and B, find A B, A B, and ... (the complement of A). A and B are subsets of the set of all positive integers, {1, 2, 3, . . .}, with A={1, 2, 6, 10} and B={2, 4, 5}.
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6.3.4 For the given sets A and B, find A B, A B, and ... (the complement of A). A and B are subsets of the set of all positive integers, {1, 2, 3, . . .}, with set A being all even numbers and set B being all multiples of 3.
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6.3.5 For the given sets and sample spaces, show that the assignment of probabilities is mathematically consistent and use them to compute the requested probability. The sample space is S={0, 1, 2, 3, 4}. Suppose that Pr({0}) = 0.2 Pr({1}) = 0.3 Pr({2}) = 0.4 Pr({3}) = 0.1 Pr({4}) = 0.0. Find Pr(A) and ...if A={0, 1, 2} and Pr(B) if B={0, 2, 4}. Is Pr(A ∪ B)=Pr(A) + Pr(B)? Why or why not?
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6.3.6 For the given sets and sample spaces, show that the assignment of probabilities is mathematically consistent and use them to compute the requested probability. The sample space is S={0, 1, 2, 3, 4}. Suppose that Pr({0}) = 0.1 Pr({1}) = 0.3 Pr({2}) = 0.4 Pr({3}) = 0.1 Pr({4}) = 0.1. Find Pr(A) and Pr(Ac) if A={0, 2} and Pr(B) if B={3, 4}. Is Pr(A ∪ B)=Pr(A) + Pr(B)? Why or why not?
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6.3.7 For the given sets and sample spaces, show that the assignment of probabilities is mathematically consistent and use them to compute the requested probability. The sample space is S={0, 1, 2, 3, 4}. Suppose that Pr({0})= 0.2, Pr({1})=0.1, Pr({2})=0.4, and Pr({3})=0.1. Find Pr(A) and ...if A={4} and Pr(B) if B={3, 4}.
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6.3.8 For the given sets and sample spaces, show that the assignment of probabilities is mathematically consistent and use them to compute the requested probability. The sample space is S={0, 1, 2, 3, 4}. Suppose that Pr({0})= 0.3, Pr({1})=0.2, Pr({2})=0.4, and Pr({4})=0.1. Find Pr({3}), Pr({1,2,3}), and Pr({2,4}).
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6.3.9 Draw Venn diagrams with sets A, B, and C satisfying the following requirements. A and B disjoint, B and C disjoint, A and C not disjoint.
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6.3.10 Draw Venn diagrams with sets A, B, and C satisfying the following requirements. A and B disjoint, B and C not disjoint, A and C not disjoint.
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6.3.11 Draw Venn diagrams with sets A, B, and C satisfying the following requirements. No two sets disjoint, but A∩B∩C empty.
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6.3.12 Draw Venn diagrams with sets A, B, and C satisfying the following requirements. No two sets disjoint, and A∩B∩C nonempty.
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6.3.13 The following formula gives the probability of the union of any two events, whether or not they are disjoint, Pr(A ∪ B)=Pr(A) + Pr(B) − Pr(A ∩ B). As indicated in the figure, adding the area in A and B counts the area in the intersection A B twice. Subtracting the area of the intersection corrects for this double counting. ... Test this formula on the following examples. The sets A and B in Exercise 5.
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6.3.14 The following formula gives the probability of the union of any two events, whether or not they are disjoint, Pr(A ∪ B)=Pr(A) + Pr(B) − Pr(A ∩ B). As indicated in the figure, adding the area in A and B counts the area in the intersection A B twice. Subtracting the area of the intersection corrects for this double counting. ... Test this formula on the following examples. The sets A and B in Exercise 6.
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6.3.15 The following formula gives the probability of the union of any two events, whether or not they are disjoint, Pr(A ∪ B)=Pr(A) + Pr(B) − Pr(A ∩ B). As indicated in the figure, adding the area in A and B counts the area in the intersection A B twice. Subtracting the area of the intersection corrects for this double counting. ... Test this formula on the following examples. Using the probabilities in Exercise 5, check the formula on the sets C={1, 2, 3} and D={0, 1, 2}.
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6.3.16 The following formula gives the probability of the union of any two events, whether or not they are disjoint, Pr(A ∪ B)=Pr(A) + Pr(B) − Pr(A ∩ B). As indicated in the figure, adding the area in A and B counts the area in the intersection A B twice. Subtracting the area of the intersection corrects for this double counting. ... Test this formula on the following examples. Using the probabilities in Exercise 6, check the formula on the sets C={2, 3, 4} and D={0, 1, 2}.
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6.3.17 Give the sample spaces associated with the following experiments. Say how many simple events there are and list them if there are fewer than ten. If there are more than ten, list three simple events. We cross two plants with genotype bB and check the genotype of one offspring.
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6.3.18 Give the sample spaces associated with the following experiments. Say how many simple events there are and list them if there are fewer than ten. If there are more than ten, list three simple events. We cross two plants with genotype bB and check the genotype of two offspring.
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6.3.19 Give the sample spaces associated with the following experiments. Say how many simple events there are and list them if there are fewer than ten. If there are more than ten, list three simple events. A molecule jumps in and out of a cell. We record whether the molecule is inside or outside the cell at times 1 and 5.
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6.3.20 Give the sample spaces associated with the following experiments. Say how many simple events there are and list them if there are fewer than ten. If there are more than ten, list three simple events. A molecule jumps in and out of a cell. We record whether the molecule is inside or outside the cell at times 2, 5, and 10.
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6.3.21 Give the sample spaces associated with the following experiments. Say how many simple events there are and list them if there are fewer than ten. If there are more than ten, list three simple events. Two molecules jump in and out of a cell. We record how many molecules are inside at times 1 and 5.
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6.3.22 Give the sample spaces associated with the following experiments. Say how many simple events there are and list them if there are fewer than ten. If there are more than ten, list three simple events. Three molecules jump in and out of a cell. We record how many molecules are inside at times 3 and 5.
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6.3.23 Give the sample spaces associated with the following experiments. Say how many simple events there are and list them if there are fewer than ten. If there are more than ten, list three simple events. We count how many out of 16 plants are taller than 50 cm.
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6.3.24 Give the sample spaces associated with the following experiments. Say how many simple events there are and list them if there are fewer than ten. If there are more than ten, list three simple events. We measure the heights of two plants.
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6.3.25 We start 100 molecules in a cell and count the number, N, that remain after 10 minutes. Give five simple events that are included in the following events. N <10.
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6.3.26 We start 100 molecules in a cell and count the number, N, that remain after 10 minutes. Give five simple events that are included in the following events. N >90.
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6.3.27 We start 100 molecules in a cell and count the number, N, that remain after 10 minutes. Give five simple events that are included in the following events. N is odd
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6.3.28 We start 100 molecules in a cell and count the number, N, that remain after 10 minutes. Give five simple events that are included in the following events. 30≤ N ≤32 or 68≤ N ≤70.
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6.3.29 We start 100 molecules in a cell and count the number, N , that remain after 10 minutes. Find the union and intersection of the following events. Event A is N <10, and event B is N >5.
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6.3.30 We start 100 molecules in a cell and count the number, N , that remain after 10 minutes. Find the union and intersection of the following events. Event A is N >10, and event B is N <5.
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6.3.31 We start 100 molecules in a cell and count the number, N , that remain after 10 minutes. Find the union and intersection of the following events. Event A is N >10, and event B is N >5.
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6.3.32 We start 100 molecules in a cell and count the number, N , that remain after 10 minutes. Find the union and intersection of the following events. Event A is 20> N >10, and event B is 15> N >5.
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6.3.33 We follow four individually labeled molecules and record the minute '...when molecule i leaves the cell. For example, if ... ...the first molecule left during minute 1, the second left during minute 3, the third left during minute 6, and the fourth left during minute 2. Give three simple events that are included in the following events. All molecules left before minute 5.
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6.3.34 We follow four individually labeled molecules and record the minute '...when molecule i leaves the cell. For example, if ... ...the first molecule left during minute 1, the second left during minute 3, the third left during minute 6, and the fourth left during minute 2. Give three simple events that are included in the following events. Molecules 1, 2, and 4 left before minute 5, and molecule 3 left after minute 7.
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6.3.35 We follow four individually labeled molecules and record the minute '...when molecule i leaves the cell. For example, if ... ...the first molecule left during minute 1, the second left during minute 3, the third left during minute 6, and the fourth left during minute 2. Give three simple events that are included in the following events. All odd-numbered molecules left at odd times.
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6.3.36 We follow four individually labeled molecules and record the minute '...when molecule i leaves the cell. For example, if ... ...the first molecule left during minute 1, the second left during minute 3, the third left during minute 6, and the fourth left during minute 2. Give three simple events that are included in the following events. All odd-numbered molecules left at odd times, and all evennumbered molecules left at even times.
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6.3.37 Give two mathematically consistent ways of assigning probabilities to the results of the following experiments. Try to make one of your assignments biologically reasonable. The situation in Exercise 17. Exercise 17 We cross two plants with genotype bB and check the genotype of one offspring.
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6.3.38 Give two mathematically consistent ways of assigning probabilities to the results of the following experiments. Try to make one of your assignments biologically reasonable. The situation in Exercise 18.Exercise 18 We cross two plants with genotype bB and check the genotype of two offspring.
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6.3.39 Give two assignments, different from those in the text, of probabilities when counting the number of molecules inside a cell starting from an initial number of 3. Compute Pr(N is odd) and Pr(N ≠1) in each case. Create an assignment where Pr(N =1) is larger than the probability of any other simple event (but none is zero).
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6.3.40 Give two assignments, different from those in the text, of probabilities when counting the number of molecules inside a cell starting from an initial number of 3. Compute Pr(N is odd) and Pr(N ≠1) in each case. Create an assignment where Pr(N =1) is equal to the probability of each other simple event.
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6.3.41 Give two assignments, different from those in the text, of probabilities when counting the number of molecules inside a cell starting from an initial number of 3. Compute Pr(N is odd) and Pr(N ≠1) in each case. Create an assignment where Pr(N =1) is smaller than the probability of any other simple event, but not equal to 0.
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6.3.42 Give two assignments, different from those in the text, of probabilities when counting the number of molecules inside a cell starting from an initial number of 3. Compute Pr(N is odd) and Pr(N ≠1) in each case. Create an assignment where the probabilities get larger as the number of molecules gets larger.
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