In Exercises 1-4, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate.
3. Experiment: Choosing a month of the year
Event: Choosing a month that begins with the letter J

Verified step by step guidance

1. Step 1: Understand the problem. The probability experiment involves choosing a month of the year, and the event is choosing a month that begins with the letter 'J'. There are 12 months in a year, and we need to identify which of these months meet the criteria of starting with 'J'.
2. Step 2: Identify the sample space. The sample space is the set of all possible outcomes of the experiment, which includes all 12 months: {January, February, March, April, May, June, July, August, September, October, November, December}.
3. Step 3: Determine the subset of the sample space that satisfies the event condition. The months that begin with the letter 'J' are {January, June, July}.
4. Step 4: Count the number of outcomes in the event. The subset {January, June, July} contains 3 outcomes, so the number of outcomes in the event is 3.
5. Step 5: Draw a tree diagram if needed. A tree diagram can visually represent the choices. Start with a single branch for the experiment (choosing a month), then create branches for each month, and highlight the branches corresponding to January, June, and July to show the event.

Key Concepts

Sample Space

The sample space of a probability experiment is the set of all possible outcomes. In the context of choosing a month of the year, the sample space consists of the twelve months: January, February, March, April, May, June, July, August, September, October, November, and December. Understanding the sample space is crucial for calculating probabilities and determining the likelihood of specific events.

Event

An event is a specific outcome or a set of outcomes from the sample space that we are interested in. In this case, the event is choosing a month that begins with the letter 'J', which includes January and June. Identifying the event helps in calculating the probability of its occurrence based on the sample space.

Tree Diagram

A tree diagram is a visual representation used to illustrate all possible outcomes of a probability experiment. It branches out from a starting point, showing each possible outcome at each stage. In this scenario, while a tree diagram may not be necessary for a single selection of a month, it can be useful for more complex experiments involving multiple choices or events.