We can use simulation to examine the fate of populations of living creatures. Consider the Asian stochastic beetle. Females of this insect have the following pattern of reproduction: • 20% of females die without female offspring, 30% have one female offspring, and 50% have two female offspring. • Different females reproduce independently. What will happen to the population of Asian stochastic beetles: will they increase rapidly, barely hold their own, or die out? It is enough to look at the female beetles, as long as there are some males around. Assign digits to simulate the offspring of one female beetle. Select all that apply. Assign 2, 0, 3 to no female offspring, 1, 9 to one female offspring, 8, 6, 7, 5, 4 to two female offspring. Assign 0, 1 to no female offspring, 0, 1, 2 to one female offspring, 0, 1, 2, 3, 4 to two female offspring. Assign 0, 1, 2 to no female offspring, 8, 9 to one female offspring, 3, 4, 5, 6, 7 to two female offspring. Assign 0, 1 to no female offspring, 2, 3, 4 to one female offspring, 5, 6, 7, 8, 9 to two female offspring. 담 Raining now (₂) 2:49 PM

Introduction: It is required to choose the correct option regarding assigning digits for the simulation.Explanation: It is given that 20% of the females give birth to no female offspring, 30% give birth to one female offspring, and 50% give birth to two female offspring. There are 10 single digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Now: 20% of 10=20100×10=2;30% of 10=30100×10=3;50% of 10=50100×10=5. Also, 20% + 30% +50% = 100%, and 2 + 3 + 5 = 10. Therefore, single digits must be assigned in such a way that 20% or 2 of the 10 single digits are assigned to no female offspring, 30% or 3 of the 10 single digits are assigned to one female offspring, and 50% or 5 of the 10 single digits are assigned to two female offspring. The first and third options assign 3 single digits to no female offspring, and 2 single digits to one female offspring. Therefore, these options are not correct. Note that, since the percentages add up to 100%, these three are the only possibilities regarding having female offspring. Further, these three categories are mutually exclusive, since it is impossible to belong to more than one of these three categories. For example, it is not possible to have no female offspring and also one female offspring. Due to being mutually exclusive, the random numbers assigned to one category must not be attached to any other category. The second option assigns the single digits 0 and 1 to all three categories. During simulation, if 0 or 1 comes up, it would become impossible to decide whether it represents females with no female offspring, one female offspring, or two female offspring. Therefore, the second option is not correct. The fourth option assigns the single digits 0 and 1 to the category of no female offspring, different single digits 2, 3, 4 to one female offspring, and another set of different single digits, 5, 6, 7, 8, 9 to two female offspring. No digit is repeated. This satisfies all the criteria for assignment. The fifth option assigns the single digits 1 and 5 to the category of no female offspring, different single digits 3, 6, 9 to one female offspring, and another set of different single digits, 0, 2, 4, 7, 8 to two female offspring. No digit is repeated. This satisfies all the criteria for assignment. Both the fourth and fifth options ensure that 20% or 2 of the 10 single digits are assigned to no female offspring, 30% or 3 of the 10 single digits are assigned to one female offspring, 50% or 5 of the 10 single digits are assigned to two female offspring, and no digit is assigned to more than one category. Thus, the correct options are the fourth and fifth options from the top.

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