A large governmental survey of dental care among children 2 to 17 years old found the following distribution of times since last visit to the dentist:
(1st column)Time since last visit
(1st column)6 months or less
(1st column)>6 months but no more than 1 year
(1st column)>1 year but no more than 2 years
(1st column)>2 years but no more than 5 years
(1st column)More than 5 years
(2nd Column)Probability
(2nd Column).57
(2nd Column).18
(2nd Column).08
(2nd Column).03
(2nd Column) ?
Questions:
(a) What must be the probability that a child has seen a dentist in more than 5 years? _________
(b) What is the prob. that a randomly chosen child has not seen a dentist within the last 6 months? __________
(c) What is the probability that the child has seen a dentist within one year? _____________
(a) What must be the probability that a child has seen a dentist in more than 5 years?
Based on the information given, the probability for "More than 5 years" is not provided. So, to calculate the probability, we need that missing value.
(b) What is the prob. that a randomly chosen child has not seen a dentist within the last 6 months?
The probability is 0.57. However, I must say, that's a long time to go without brushing your teeth! Maybe they've been busy inventing a toothbrush that can brush your teeth while you sleep?
(c) What is the probability that the child has seen a dentist within one year?
The probability is 0.57 + 0.18 = 0.75. So, there's a 75% chance that the child has seen a dentist within one year. Of course, it's always good to go for regular check-ups and avoid late-night dentist appointments!
To answer these questions, you can use the probabilities given in the distribution table for times since the last visit to the dentist.
(a) The probability that a child has seen a dentist in more than 5 years is represented by the last entry in the second column of the distribution table. However, the value for this entry is missing in your question. Please provide the value for the last entry in the second column, and I will calculate the probability for you.
(b) To find the probability that a randomly chosen child has not seen a dentist within the last 6 months, you need to sum up the probabilities for the first two categories in the distribution table.
Probability = Probability of "6 months or less" + Probability of ">6 months but no more than 1 year"
(c) To find the probability that a child has seen a dentist within one year, you need to sum up the probabilities for the first three categories in the distribution table.
Probability = Probability of "6 months or less" + Probability of ">6 months but no more than 1 year" + Probability of ">1 year but no more than 2 years"
Please provide the missing value in the second column, and I will calculate the probabilities for you.