Number of BirthsThe graph of the discrete probability distribution below represents the number of live births by a mother 50–54 years old who had a live birth in 2017.


c. What is the probability that a randomly selected mother aged 50 to 54 who had a live birth in 2017 was having her sixth child or more?

Verified step by step guidance

1. Identify the probabilities for the number of live births starting from the sixth child to the tenth child from the graph. These probabilities correspond to child numbers 6, 7, 8, 9, and 10.
2. Write down the probabilities for each of these child numbers as given in the graph: \(P(6)\), \(P(7)\), \(P(8)\), \(P(9)\), and \(P(10)\).
3. Since the question asks for the probability that a mother is having her sixth child or more, you need to find the sum of these probabilities: \(P(6 \text{ or more}) = P(6) + P(7) + P(8) + P(9) + P(10)\).
4. Add the probabilities together to get the total probability for having the sixth child or more. This sum represents the combined probability of all these events.
5. Interpret the result as the probability that a randomly selected mother aged 50 to 54 who had a live birth in 2017 was having her sixth child or more.

Key Concepts

Discrete Probability Distribution

A discrete probability distribution assigns probabilities to distinct, separate outcomes, such as the number of live births. Each outcome has a probability between 0 and 1, and the sum of all probabilities equals 1. This distribution helps us understand the likelihood of each specific number of births.

Calculating Probability for Multiple Outcomes

To find the probability of an event involving multiple outcomes, such as having six or more children, sum the probabilities of all relevant outcomes. For example, add the probabilities for 6, 7, 8, 9, and 10 children to get the total probability of six or more births.

Interpreting Probability from a Graph

Reading probabilities from a graph involves identifying the height of bars or points corresponding to each outcome. In this graph, the vertical axis shows probability values, and the horizontal axis shows child numbers, allowing us to extract exact probabilities for each number of births.