What is the probability that an infant will have one or more episodes of otitis media by the end of the ninth month of life given that no episodes have been observed by the end of the third month of life?

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