About a question asked in Forum

It was like:
A survey among 1000 Canadian sports fans was conducted and found out that each of them either a hockey fan or a lacrosse fan. 800 of them are hockey fans and 200 of them lacrosse fan. hence what's the probability of not being a hockey fan given that he/she is a lacrosse fan?
Someone complained of insufficient info. Though info is complete. As I finished typing and submitting the answer the question disappeared. Here's the solution for the student in need.
Among 1000 Canadian sports fans 800 are hockey fans, some of them are lacrosse fans , too some of them only hockey fans since there is none who is fan of neither hockey nor lacrosse
Therefore, (1000-800) = 200 are only lacrosse fans
Among 600 of lacrosse fans, 200 are only lacrosse fans, hence (600-200)= 400 are both fans of hockey and lacrosse
Therefore, only 800-400=400 are only hockey fans
Hence among 1000 sports fans 400 are only hockey fans, 200 are only lacrosse fans and 400 are both hockey and lacrosse fans.
thus the probability of being only lacrosse fan is 200 in 1000 =1/5 or 0.2
otherwise, probability of being only hockey fan is 400 in 1000 =2/5 or 0.4
and probability of being both hockey fan and lacrosse fan is also 400 in 1000=2/5 or 0.4
Therefore, probality of being a hockey fan anyway is = 0.4+0.4=0.8
And probability of not being a hockey fan given that he/she is a lacrosse fan = 1-0.8= 0.2.


Sanhita M.

Mathematics and Geology

20+ hours
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