Gestation Period versus Weight The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation.


d. What is the probability that a randomly selected baby born in 2017 weighed 3000–3999 grams or was postterm?

Verified step by step guidance

1. Step 1: Identify the total number of babies born in 2017 from the table. This is the grand total at the bottom right corner, which is 3,855,500.
2. Step 2: Determine the number of babies who weighed between 3000 and 3999 grams. From the table, this total is 2,511,694.
3. Step 3: Determine the number of babies who were postterm. From the table, the total number of postterm babies is 219,124.
4. Step 4: Find the overlap between babies who weighed 3000–3999 grams and were postterm, to avoid double counting. From the table, the number of postterm babies in the 3000–3999 grams category is 155,098.
5. Step 5: Use the formula for the probability of the union of two events A and B: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] where: - \(P(A)\) is the probability a baby weighed 3000–3999 grams, - \(P(B)\) is the probability a baby was postterm, - \(P(A \cap B)\) is the probability a baby was postterm and weighed 3000–3999 grams. Calculate each probability by dividing the counts by the total number of babies, then substitute into the formula.

Key Concepts

Probability of Combined Events

This concept involves finding the probability that an outcome satisfies at least one of multiple conditions, such as being in a specific weight range or gestation period. It often requires using the addition rule for probabilities, accounting for any overlap between events to avoid double counting.

Marginal and Joint Frequencies

Marginal frequencies are totals for a single category (e.g., total babies in a weight range), while joint frequencies represent counts for combined categories (e.g., babies in a weight range and a gestation period). Understanding these helps calculate probabilities from contingency tables.

Complement and Overlap in Probability

When calculating the probability of 'A or B,' it is important to subtract the overlap (A and B) to avoid double counting. This ensures the correct combined probability, especially when events are not mutually exclusive, as in the case of weight categories and gestation periods.