In a community experiencing a Zumba virus epidemic, we get: Probability that a p
ID: 3124351 • Letter: I
Question
In a community experiencing a Zumba virus epidemic, we get:
Probability that a person exposed to the Zumba virus gets infected = 0.85
Probability that a person infected by the virus will favor a Latin dance style = 0.45
Probability that a person infected with the virus will favor a hip-hop style = 0.22
(Note that a particular person can favor only one dance style!)
For all the questions below, answer in decimal fractions, not percentages, and use three decimal places. E.g.: 0.333.
1. If four people are exposed to the virus, what's the chance they'll all be infected?
2. If four people are exposed to the virus, what's the chance at least one will be infected?
3. If a person is exposed to the virus, what's the chance they'll end up infected and favoring a Latin dance style?
4. If a person is exposed to the virus, what's the chance they'll end up infected and favoring either a Latin or hip-hop dance style?
5. If two people are exposed, what's the chance they'll both end up infected and favoring a Latin style?
6. If two people are exposed, what's the chance that they'll both be infected, but one will favor Latin and one will favor hip-hop?
7. For someone infected with the Zumba virus, the probability they'll be dancing the samba (assuming they're dancing at all) is 0.18. For someone not infected, the probability they'll dance the samba (again, if they're dancing) is just 0.02. If you go to a club where everyone is dancing and where the fraction of people infected is 0.08, what's the chance that someone dancing the samba is infected with the virus? Give your answer in the same three-decimal-place style as above.
Explanation / Answer
0.85^4
=0.522
2.If four people are exposed to the virus, the chance that at least one will be infected is:
(1-0.85)^3*0.85+(1-0.85)^2*0.85^2+(1-0.85)*0.85^3
=0.111
3.If a person is exposed to the virus, then the chance that they'll end up infected and favoring a Latin dance style is:
0.85*0.45=0.3825