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2 June, 04:53

A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Three hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks

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  1. 2 June, 05:05
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    The number of mice that will be infected next week are 130 while

    The number of mice that will be infected in 3 weeks are 111

    Step-by-step explanation:

    From the information given, the researcher is studying the spread of a virus in a population of 1000 laboratory mice. i. e, n = 1000

    Number of infected = 300

    Non infected = 1000 - 300 = 700

    Probability an infected mouse will overcome = 80% = 0.8

    Probability a noninfected mouse becomes infected = 10% = 0.10

    The number of infected that will overcome = 0.8 * 300 = 240

    The number of non infected that will become infected = 0.1 * 700 = 70

    The number that will be infected on the first week =

    300 - 240 + 70

    = 130

    Number that will be healthy on the first week =

    700 + 240 - 70

    = 870

    Calculating for week 2:

    The number of infected that will overcome = 0.8 * 130 = 104

    The number of non infected that will become infected = 0.10 * 870 = 87

    The number that will be infected on the second week =

    130 - 104 + 87

    = 113

    Number that will be healthy on the second week =

    870 + 107 - 87

    = 887

    Calculating for week 3:

    The number of infected that will overcome = 0.8 * 113 = 90.4

    The number of non infected that will become infected = 0.10 * 887 = 88.7

    The number that will be infected on the third week =

    113 - 90.4 + 88.7

    = 111.3 ≈ 111

    Number that will be healthy on the third week =

    887 + 90.4 - 88.7

    = 888.7 ≈ 889

    From our calculations, the number of mice that will be infected next week are 130

    The number of mice that will be infected in 3 weeks are 111
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