Finding Classical Probabilities In Exercises 41-46, a probability...

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

1:54 minutes

Problem 3.1.43

Textbook Question

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.
43. Event C: rolling a number greater than 4

Verified step by step guidance

Step 1: Understand the problem. The experiment involves rolling a 12-sided die, and we are tasked with finding the probability of rolling a number greater than 4. Classical probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes.

Step 2: Identify the total number of possible outcomes. Since the die is 12-sided, the total number of outcomes is 12. This represents all the numbers from 1 to 12.

Step 3: Determine the favorable outcomes. The event 'rolling a number greater than 4' includes all numbers greater than 4, which are {5, 6, 7, 8, 9, 10, 11, 12}. Count these numbers to find the number of favorable outcomes.

Step 4: Write the formula for classical probability. The probability of an event is given by:

\frac{Number of favorable outcomes}{Total number of possible outcomes}

Step 5: Substitute the values into the formula. The number of favorable outcomes is the count of numbers greater than 4, and the total number of possible outcomes is 12. Simplify the fraction to express the probability.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Classical Probability

Classical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in a probability experiment. It assumes that all outcomes are equally likely. For example, when rolling a 12-sided die, the total outcomes are 12, and the probability of rolling a specific number is 1/12.

Favorable Outcomes

Favorable outcomes refer to the specific results of an experiment that satisfy the conditions of the event being analyzed. In the context of rolling a die, if the event is rolling a number greater than 4, the favorable outcomes would be the numbers 5, 6, 7, 8, 9, 10, 11, and 12, totaling 8 favorable outcomes.

Calculating Probability

To calculate the probability of an event, you divide the number of favorable outcomes by the total number of possible outcomes. For the event of rolling a number greater than 4 on a 12-sided die, the probability would be calculated as 8 (favorable outcomes) divided by 12 (total outcomes), resulting in a probability of 2/3.

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Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.43. Event C: rolling a number greater than 4