Suppose an “otitis-prone family” is defined as one in which at least three siblings of five develop otitis media in the first 6 months of life. What proportion of five-sibling families is otitis prone if we assume the disease occurs independently for different siblings in a family?

Pediatrics, Otolaryngology
Otitis media is a disease that occurs frequently in the first few years of life and is one of the most common reasons for physician visits after the routine checkup. A study was conducted to assess the frequency of otitis media in the general population in the first year of life. Table 4.16 gives the number of infants of 2500 infants who were first seen at birth who remained disease-free by the end of the ith month of life, i = 0, 1, . . . , 12. (Assume no infants have been lost to follow-up.)

Table 4.16: Number of infants (of 2500) who remain disease-free at the end of each month during the first year of life

__________________________ Disease-free infants at
i ................................................ 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