probality that a new policyholder will have an accident

[mark]

I was wondering if anyone could help me with this problem

the problem says, An insurance company believes that people can be divided into two classes: those who are accident-prone person will have an accident at some time within a fixed 1-year period with a probability 0.4, whereas this probability decrease to 0.2 for a non-accident-prone person. If we assume that 30% of the population is accident prone,

what is the probability that a new policyholder will have an accident within a year of purchasing a policy?

i think that this problem involves binomal distrubtion, so i did

let x = # of policyholders that will have an accident

p(accident prone ) = .4
p(non-accident prone) =.2

p = .4
q = .2

p(x greater than or equal to 1), but i can't figure out what n should be in this problem

 

[pka]

Suppose that X means ‘prone to an accident’ and that Y means ‘has an accident’. Then P(Y|X)=0.4, P(Y|X’)=0.2, and P(X)=0.3.

Putting this together we can get: P(YX)=0.12 and P(YX’)=0.14.
Can you use these to find P(Y)?

 

[mark]

is it p(y) = p(x)p(y|x) + p(x')p(y|x')

 

[pka]

Yes, of course that is it.