Question

The number of earthquakes in California and Alaska follows a Poisson Process with an average of 4 earthquakes per week and 3 earthquakes per week respectively. One of these states is chosen at random and it is learned that 6 earthquakes occurred in one week. What is the probability that the state of Alaska was chosen?

Answer 1

California 1.   Alaska. 2

We know    Poisson distribution

for California P(x=6) =

   P(x=6) = 0.018315639 *4096/ 720

= 0.104195635

similarly for Alaska P(x=6) = 0.049787068 *729/720

= 0.050409407

California		Alaska
P (C ) =	(1/2)	P(A)=	(1/2)	6E= 6 earthquakes
P (C /6 E) =	0.1041956	P(A/6E)=	0.050409
P(6E) =	P (C ) *	P (C /6 E) +	P(A) *	P(A/6E)
P(6E) =	0.052097818	(+)	0.025204704
P(6E) =	0.077302521
	P(6E/A)=	P(A)* P(A/6E)/P(6E)
	P(6E/A)=	0.326053	Answer