Math Problem Statement

A bag has six balls labeled A, B, C, D, E, and F. One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space and list all outcomes for the event of choosing a letter from D to F.

Solution

Let's analyze the image.

The problem involves a bag with six balls, each labeled with the letters A,B,C,D,E,FA, B, C, D, E, F. A ball is chosen randomly, and the goal is to find two things:

  1. The sample space (the set of all possible outcomes when one ball is chosen).
  2. The event of choosing a letter from DD to FF.

Solution:

  1. Sample Space: The sample space includes all possible outcomes, which are the letters on the six balls. Therefore, the sample space is: Sample space={A,B,C,D,E,F}\text{Sample space} = \{ A, B, C, D, E, F \}

  2. Event of choosing a letter from DD to FF: The letters in this event are D,E,FD, E, F. So, the set for this event is: Event of choosing a letter from D to F={D,E,F}\text{Event of choosing a letter from } D \text{ to } F = \{ D, E, F \}

If you need further clarifications or details, let me know!


Here are 5 related questions to consider:

  1. What is the probability of choosing a letter AA from the sample space?
  2. What is the probability of choosing any letter between DD and FF?
  3. How would the sample space change if two balls were chosen instead of one?
  4. What would the event look like if we selected letters only from AA to CC?
  5. How would the problem change if the balls were not labeled with letters but with numbers?

Tip: In probability, events are often subsets of the sample space, and understanding how to define the event clearly helps in calculating the probability more easily!

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Math Problem Analysis

Mathematical Concepts

Probability
Sample Space
Event

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8