Question

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

Answer 1

To calculate the number of mice that will be infected next week, we need to consider the probabilities given in the question. There are currently 300 infected mice out of 1000 total mice, so the probability of a mouse being infected is 0.3.

Step-by-step explanation:

To calculate the number of mice that will be infected next week, we need to consider the probabilities given in the question. There are currently 300 infected mice out of 1000 total mice, so the probability of a mouse being infected is 300/1000 = 0.3. During the next week, 80% of the infected mice will overcome the virus, so 0.8 * 300 = 240 mice will recover. During the same week, 10% of the noninfected mice will become infected, so 0.1 * (1000 - 300) = 70 mice will become infected.

To calculate the number of mice that will be infected in 3 weeks, we can repeat this process. After the first week, we have 240 infected mice left. Following the same probabilities, we would have 0.8 * 240 = 192 recovering and 0.1 * (1000 - 240) = 76 becoming infected in the second week. In the third week, we would have 0.8 * 192 = 154 recovering and 0.1 * (1000 - 240 - 192) = 56 becoming infected.

Therefore, next week there will be 240 infected mice and in 3 weeks there will be 56 infected mice.

Answer 2

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