In: Statistics and Probability
At one point during the COVID-19 crisis, the probability that an person who tested positive for the illness would infect another person they came into contact with was 75% . Suppose on that day, the infected person came into contact with 15 other people.
For each part below, show the formula set-up and round your final answers to four decimal places.
a) The probability the ill person infected exactly 10 people out of the 15.
b) the probability the ill person infected at most 2 of the 15 people.
c) the probability the ill person infected at least 3 people out of the 15.
d) what are the expected number of people the ill person will infect? Round to the nearest whole number.