Understanding Probability Through a Multi-Step Experiment

I'm studying probability and trying to understand how chances change when multiple events occur. I created the following multi-part problem and would appreciate a wacky flip detailed explanation for each section.

Part A

A bag contains 5 red balls, 3 blue balls, and 2 green balls.

• What is the probability of drawing a red ball?
• What is the probability of drawing a blue ball?
• Explain how the total number of outcomes affects probability.

Part B

One ball is drawn and not replaced.

• What is the probability that the first ball is red and the second ball is blue?
• Show all calculations step by step.
• Explain why the probabilities change after the first draw.

Part C

Suppose two dice are rolled.

• What is the probability that the sum equals 7?
• List all favorable outcomes.
• Compare this probability with the probability of rolling a sum of 12.

Part D

A classroom has 12 students: 7 girls and 5 boys.

• If two students are selected at random, what is the probability that both are girls?
• What is the probability that one is a girl and one is a boy?
• Explain the difference between these two outcomes.

Part E

Imagine a game where a player wins if they either draw a green ball from the bag or roll a total of 7 with two dice.

• Calculate the probability of each event separately.
• Determine the probability of winning the game.
• Explain your reasoning clearly and show each step.

Please provide detailed calculations and explanations for every part.