probability (1 Viewer)

[kunny funt]

There are two events A and B. Probability of at least one of the two is 0.1 and probability of exactly one of the two is 0.08. Then what is the probability of both A and B?

 

[Templar]

I guess 0.02

 

[withoutaface]

A+b=.1
A+b-ab=.08=.1-.02

:.ab=.02

 

[Archman]

A+b=.1
A+b-ab=.08=.1-.02

:.ab=.02

p(exactly one happening)=p(at least one happening) - p(both happening)
so it is 0.02
but withoutaface had the wrong reasoning
the chance of at least one happening is not a+b
it's 1-p(none happening) = 1-(1-a)(1-b) = a+b-ab

while the chance of exactly one happening is not a+b-ab
it is a(1-b)+b(1-a) = a+b-2ab

 

[Trev]

the answers still right though

 

[Templar]

the answers still right though

Method is what's important. The correct solution is just a bonus.

 

[withoutaface]

p(exactly one happening)=p(at least one happening) - p(both happening)
so it is 0.02
but withoutaface had the wrong reasoning
the chance of at least one happening is not a+b
it's 1-p(none happening) = 1-(1-a)(1-b) = a+b-ab

while the chance of exactly one happening is not a+b-ab
it is a(1-b)+b(1-a) = a+b-2ab

Thanks for that archman, poor technique's fucked me up too many times in the past. :-/

 

[kunny funt]

i used a venn diagram which made it reasonably easy to understand:

p(at least one happening) = p(A or B) = 0.10 (area made by two circles)

p(exactly one) = p[(A and 1-B) or (1-A and B)] (area as above minus the overlap)
= 0.08

Therefore P(A and B) is the overlap which is 0.10 - 08 = 0.02 .....

 

[JamiL]

that seems 2 be a 2unit question in which u can use a vent diagram... quiet easy 4 4u...