Favorable Outcomes

Definition

Favorable outcomes refer to the desirable or positive results that are expected or hoped for in a particular situation or experiment. In the context of probability and statistics, favorable outcomes are the specific outcomes that are considered successful or favorable based on the given criteria or goals.

5 Must Know Facts For Your Next Test

1. The probability of a favorable outcome is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in the sample space.
2. Favorable outcomes are often represented by the symbol $A$ or $E$, and the probability of a favorable outcome is denoted as $P(A)$ or $P(E)$.
3. In a dice experiment using three regular dice, the favorable outcomes are the specific combinations of the three dice that meet the desired criteria or goals.
4. The number of favorable outcomes in a dice experiment can be determined by carefully analyzing the possible combinations and identifying those that satisfy the given conditions.
5. Favorable outcomes are an essential concept in understanding discrete probability distributions, as they form the basis for calculating the probability of specific events occurring.

Review Questions

• Explain how the concept of favorable outcomes relates to the probability of an event occurring in a dice experiment using three regular dice.
  • In a dice experiment using three regular dice, the favorable outcomes are the specific combinations of the three dice that meet the desired criteria or goals. The probability of a favorable outcome is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in the sample space. For example, if the goal is to roll a sum of 12 with the three dice, the favorable outcomes would be the specific combinations that add up to 12, such as (4, 4, 4) or (3, 5, 4). The probability of rolling a sum of 12 would then be the number of these favorable outcomes divided by the total number of possible outcomes when rolling three dice.
• Describe how the concept of favorable outcomes is used to calculate the probability distribution in a discrete probability experiment, such as the dice experiment with three regular dice.
  • The concept of favorable outcomes is central to understanding discrete probability distributions, as it forms the basis for calculating the probability of specific events occurring. In the context of the dice experiment with three regular dice, the favorable outcomes are the specific combinations of the three dice that meet the desired criteria or goals. To calculate the probability distribution, one must first identify all the possible outcomes in the sample space, then determine which of those outcomes are favorable based on the given conditions. The probability of each favorable outcome is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This process allows for the construction of the probability distribution, which describes the likelihood of each possible outcome in the experiment.
• Analyze how the concept of favorable outcomes can be used to make inferences and draw conclusions about the results of a dice experiment using three regular dice, and how this understanding can be applied to other discrete probability distributions.
  • The concept of favorable outcomes is a fundamental tool for making inferences and drawing conclusions about the results of a dice experiment using three regular dice, as well as other discrete probability distributions. By identifying the favorable outcomes, one can calculate the probability of specific events occurring, which can then be used to make predictions, test hypotheses, and draw conclusions about the underlying probability model. For example, in the dice experiment, if the goal is to roll a sum of 12, the favorable outcomes can be determined, and the probability of rolling a sum of 12 can be calculated. This information can then be used to make inferences about the likelihood of this event occurring, or to compare the probabilities of different outcomes. Furthermore, the understanding of favorable outcomes can be applied to other discrete probability distributions, such as those involving coin flips, card draws, or any other random process with a finite number of possible outcomes. The ability to identify and analyze favorable outcomes is a crucial skill in the study of probability and statistics.

Related terms

Probability:

The measure of the likelihood or chance of an event occurring, typically expressed as a number between 0 and 1.

Sample Space:

The set of all possible outcomes or results in an experiment or random process.

Mutually Exclusive Events:

Events that cannot occur simultaneously, meaning that if one event occurs, the other event(s) cannot occur.