Based upon data obtained from National Institute of Dental Research, it has been estimated that 41% of 12 year olds have never had cavity, 32% of 13 year olds have never had cavity, and 27% of 14 year olds have never had cavity.
If a child is chosen a random from group of 20 junior high school students including four 12 year olds, six 13 year olds and ten 14 year olds and this child doesn't have a cavity, determine the probability that this child is 14 years old?