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A probability model is like a blueprint that shows all possible outcomes of a random experiment along with their corresponding probabilities. It helps us understand how likely different events are.
For instance, rolling a die is a common experiment. In a fair die, each number has an equal chance of appearing. However, if the die is loaded—meaning it's biased—some numbers are more likely to show up than others.
In our case, the loaded die shows that the probability of getting a 1 or a 6 is 0.3, while rolling a 2, 3, 4, or 5 has a much lower probability of 0.1 each. This model completely describes what can happen when you roll the die and precisely how often each result will occur.

A loaded die is intentionally biased. This means it does not behave like a normal die.
In a standard die, each number, from 1 to 6, has an equal chance of being rolled. This chance is 1/6 or approximately 0.1667.
But in a loaded die, some outcomes are made more likely than others.

• This might occur due to intentional changes in the die's weight or shape, skewing results in favor of certain numbers.
• In our exercise, the probabilities are heavily loaded towards 1 and 6, both with a chance of 0.3, distorting the expected even spread of outcomes.

Understanding loaded dice can help in identifying unfair games or situations.

Outcomes in probability are simply the possible results that can occur from an experiment. For a die, the outcomes are the numbers 1 through 6.
However, the interesting part is when these outcomes are not equally likely because the die is loaded.
This changes how we look at the outcomes, as each number now carries a different weight or probability.
In our scenario, outcomes 1 and 6 are prime, each with a probability of 0.3, making them more common than the others with probabilities of 0.1. Observing these skewed results can be surprising. They influence decisions and provide insight into how the bias affects the game.

Breaking down the exercise into step-by-step solutions makes it manageable and helps ensure understanding of each part.
Let's go over this particular problem:

• **Step 1** was about identifying odd outcomes. These are specifically 1, 3, and 5, where we noted their respective probabilities.
• **Step 2** involved calculating the total probability of getting an odd number. By summing the probabilities of these outcomes, we get 0.5.
• **Step 3** applied the conditional probability formula to find the probability of rolling a 1, given the result was odd. This was calculated as 0.6.
• **Step 4** simply required matching our calculated result to the correct answer choice, which was option (e) 0.60.

This structured approach not only helps in solving this particular problem but also offers a clear strategy for tackling similar problems in the future.