Mysterious probability problem wants to solved!!!

I computed infant will have 1 or more episodes of otitis media by the end of 6^th 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 end of 9^th month given that no episodes have been observed by the end of the 3^rd 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 observation until the third month, we have 6 months of observations.
P(9^th)=.52 and p(4^th)=.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) (μ^x) / x!
But the result wasn’t as what the book said. Book answer is 0.104

Can anybody think of better way in talking this problem

Hi Yoha,

I agree with your P for 6 months and 1 year.

I think you have made two mistakes in your setup of problem a.

First of all, notice that your P(6th) and P9(th) are the same at .52 . I believe this is a simple math mistake on your part.

Second, if the infant has no otitis in month 3, he is now in a pool of 2300. In month 9 only 1300 of the 2300 are still healthy. So I believe you are looking for 1000/2300 which is .4347 .

-mpg

Hi medicalphysicsguy,

Thanks for spending a time reviewing my answers.
I wrote p(6month)=.25 because if we calculate the probability of success , it would be .75 and we are interested in calculating the q=1-.75=.25.
The procedure would be applied on the 9th month too, but I would like to ask you about your calculation, you subtracted 2300 from 1300 =1000 and divided it by 2300=.4347
You followed the simple rule of probability? Is that right?!

Once again, Thanks for your help.

what about question b. I couldn't figure it out? How can I find proportion of 5 sibling family?
Thanks