[Solved] Understanding Probability Through a Multi-Step Experiment

Assignment Prompt & Instructions

[>Probability homework help](https://www.sweetstudy.com/fields/mathematics-probability)

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](https://wackyflip2.org/) 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.