Math Problem Statement

Determine if true or false: the events are independent. A coin is flipped and lands on heads, then a die is rolled on a six. An orange peg and then a blue peg are selected at random so long as 3 children are waiting in line. A blue coloring pen is selected at random, replaced in the box, and then a green coloring pen is selected. Two different students are selected at random to read a story to the class.

Solution

I see that you've uploaded an image containing some probability-related questions. Here’s a transcription of the questions based on what I see:

  1. Determine if true or false: the events are independent.
  2. A coin is flipped and lands on heads, then a die is rolled on a six.
  3. An orange peg and then a blue peg are selected at random so long as 3 children are waiting in line.
  4. A blue coloring pen is selected at random, replaced in the box, and then a green coloring pen is selected.
  5. Two different students are selected at random to read a story to the class.

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Math Problem Analysis

Mathematical Concepts

Probability
Independent Events

Formulas

P(A and B) = P(A) * P(B) for independent events

Theorems

Multiplication Rule for Independent Events

Suitable Grade Level

Grades 9-12