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.


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

Verified step by step guidance

1. Step 1: Identify the relevant probabilities from the graph for the number of live births corresponding to the fourth and fifth child. In this case, locate the probabilities for 4 and 5 on the x-axis.
2. Step 2: Read the probability values from the graph for these two points. For example, find the probability value at 4 children and the probability value at 5 children.
3. Step 3: Since the problem asks for the probability that a mother is having either her fourth or fifth child, you need to add the two probabilities together. This is because these two events are mutually exclusive.
4. Step 4: Use the formula for the union of mutually exclusive events: \(P(4 \text{ or } 5) = P(4) + P(5)\).
5. Step 5: Add the two probabilities obtained from the graph to get the final probability that a randomly selected mother aged 50 to 54 who had a live birth in 2017 was having either her fourth or fifth child.

Key Concepts

Discrete Probability Distribution

A discrete probability distribution lists all possible outcomes of a random variable and their associated probabilities. Each probability is between 0 and 1, and the sum of all probabilities equals 1. This concept helps in understanding how likely each outcome is in a given scenario.

Calculating Probability for Multiple Outcomes

To find the probability of multiple mutually exclusive events occurring, you add their individual probabilities. For example, the probability of having either the fourth or fifth child is the sum of the probabilities of having the fourth child and having the fifth child.

Interpreting Probability Graphs

Probability graphs visually represent the likelihood of different outcomes. The height of each bar corresponds to the probability of that outcome. Understanding how to read these graphs is essential for extracting probabilities and answering related questions.