Question 1) The small country of San Lorenzo is currently experiencing an outbreak of a disease. Of the population of 200,000 people, 43,000 are currently infected. Pharmaceutical company PlaceboCorp has been selling a vaccine, and currently, 160,000 people have been vaccinated.
Someone tips you off that the vaccine is actually a placebo though (gasp) and has no effect. If being vaccinated and being infected are independent, how many people should be vaccinated and not infected?
Question 2) A team of 20 people divides up into 5 groups of 4. Each member of a group flips a fair coin - the team wins if at least one group gets all heads.
What is the probability that the team wins?
Question 3) A box contains 10 black mice and 10 white mice.
Every time someone pulls a mouse from the box, they replace it with two mice of the opposite color.
What is the probability that the first two mice removed are different colors?
Answer as a percent, rounded to one decimal place (probability 0.3451 would be given as 34.5.)
[8:34 PM, 2/5/2022] Kareena Shah: A team of 20 people divides up into 5 groups of 4. Each member of a group flips a fair coin - the team wins if at least one group gets all heads.
What is the probability that the team wins?