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

Verified step by step guidance

1. Step 1: Understand the problem context. The problem asks for the probability that a randomly selected mother aged 50 to 54 who had a live birth in 2017 was having her fourth child. This means we need to find the probability associated with the number 4 in the discrete probability distribution.
2. Step 2: Identify the relevant value on the graph. The graph shows probabilities for the number of live births (children) a mother had, with the x-axis representing the number of children and the y-axis representing the probability.
3. Step 3: Locate the probability for the fourth child. On the x-axis, find the value 4, then look at the corresponding probability value on the y-axis. According to the graph, the probability for 4 children is labeled as 0.391.
4. Step 4: Write the probability in mathematical terms. The probability that a mother had her fourth child is \(P(X=4) = 0.391\), where \(X\) is the number of children.
5. Step 5: Interpret the result. This means there is a 39.1% chance that a randomly selected mother aged 50 to 54 who had a live birth in 2017 was having her fourth child.

Key Concepts

Discrete Probability Distribution

A discrete probability distribution lists all possible outcomes of a discrete random variable and their associated probabilities. Each probability is between 0 and 1, and the sum of all probabilities equals 1. This distribution helps determine the likelihood of specific outcomes, such as the number of children a mother has.

Probability of a Specific Outcome

The probability of a specific outcome in a discrete distribution is the value assigned to that outcome. For example, the probability that a mother is having her fourth child is the probability corresponding to the number 4 in the distribution. This value directly answers questions about the likelihood of particular events.

Interpreting Graphs of Probability Distributions

Graphs of probability distributions visually represent probabilities for each outcome, often using bars or points. The height or position of each bar/point indicates the probability of that outcome. Understanding how to read these graphs allows one to quickly identify probabilities for specific values, such as the probability of having four children.