Outbreak of COVID-19
During the outbreak of COVID-19, Donald Trump arranges two individual parties for his officials not infected with COVID-19 in New York, where the other participants are all infected with COVID-19 and the officials have chance of infection.
For each party, Donald Trump randomly delegates exactly of the officials to attend. Assume that since his officials work individually, they have chance of infection to each other when they come back to their positions.
Let be the number of officials infected with COVID-19. When has the maximum value, what is the value of ?
The answer is 42.
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1 solution
After the first party, all 30 officials chosen will be infected. Let N be the number of officials from the 20 remaining "non-sick" officials who are chosen for the second party. We see that for k = 0, 1, 2, ..., 20, P(N = k) = (30 choose (30 - k))*(20 choose k) / (50 choose 30). A calculation shows that this is maximum when N = 12 (this can be done with Excel or another spreadsheet). We are looking for the maximum of the quantity N + 30. When N = 12, this maximum is 42.