Bio-statistics, Poisson distribution

[Yoha]

I'm studying Bio-statistics and I came across this problem from the textbook.It's actually answered on the back of the book, but I couldn't really get the same numbers.

i Desease-free infants at the end of month i
0 2500
1 2425
2 2375
3 2300
4 2180
5 2000
6 1875
7 1700
8 1500
9 1300
10 1250
11 1225
12 1200

I computed infant will have 1 or more episodes of otitis media by the end of 6th month and first year of life
P(6 months) =0.25
P(year)=.52

There are two questions that I couldn’t get the same result as the book said.

a- What is the probability that an infant will have one or more episodes of otitis by the en of 9th month given that no episodes have been observed by the end of the 3rd month?

b- Suppose an otitis –prone family is defined as one in which at least 3 siblings of 5 develop otitis in the first 6 monthof life. What a proportion of five-sibling family is otitis prone if we assume the disease occur independently for different siblings in a family?


My answers:
a- If we consider there was no observed until the third month, we have 6 months of observations.
P(9th)=.52 and p(4th)=.872
I tried to to answer , but it wasn’t the same as the book answer (Book answer is .435


b- We have 3 in 5 which is equal .6
So I considered this lamda and I applied it on Poisson formula P(x; μ) = (e-μ) (μx) / x!
But the result wasn’t as what the book said. Book answer is 0.104

Can anybody think of better way talking this problem!

 

[awkward]

a) 1000 infants fall ill between months 3 and 9; 2300 are healthy at the end of month 3. So...

b) Consider applying the Binomial distribution instead of Poisson.

 

[Yoha]

Thanks for your clarification.